메뉴 건너뛰기




Volumn 88, Issue , 2016, Pages 1-208

Inverse scattering theory and transmission eigenvalues

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85006043070     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611974461     Document Type: Conference Paper
Times cited : (125)

References (118)
  • 2
    • 80155171709 scopus 로고    scopus 로고
    • The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation
    • (Cited on p. 174)
    • T. AKTOSUN, D. GlNTIDES, AND V. G. PAPANICOLAOU, The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems, 27:115004 (2011). (Cited on p. 174)
    • (2011) Inverse Problems , vol.27 , pp. 115004
    • Aktosun, T.1    Glntides, D.2    Papanicolaou, V.G.3
  • 3
    • 1342329788 scopus 로고    scopus 로고
    • Why linear sampling works
    • Cited on pp. 41, 44, 63
    • T. ARENS, Why linear sampling works, Inverse Problems, 20 (2004), pp. 163-173. (Cited on pp. 41, 44, 63)
    • (2004) Inverse Problems , vol.20 , pp. 163-173
    • Arens, T.1
  • 4
    • 74349116964 scopus 로고    scopus 로고
    • The linear sampling method revisited
    • Cited on pp. ix, 41, 44
    • T. ARENS AND A. LECHLEITER, The linear sampling method revisited, J. Integral Equations Appl., 21 (2009), pp. 179-202. (Cited on pp. ix, 41, 44)
    • (2009) J. Integral Equations Appl. , vol.21 , pp. 179-202
    • Arens, T.1    Lechleiter, A.2
  • 5
    • 84989337651 scopus 로고    scopus 로고
    • PhD thesis, Ecole Polytech-nique, Palaiseau, France,. (Cited on pp. 35, 45, 51, 66, 68)
    • L. AUDIBERT, Qualitative Methods for Heterogeneous Media, PhD thesis, Ecole Polytech-nique, Palaiseau, France, 2015. (Cited on pp. 35, 45, 51, 66, 68, 165)
    • (2015) Qualitative Methods for Heterogeneous Media , pp. 165
    • Audibert, L.1
  • 6
    • 84937801547 scopus 로고    scopus 로고
    • Identifying defects in an unknown background using differential measurements
    • (Cited on pp. 35, 42, 66, 68)
    • L. AUDIBERT, A. GIRARD, AND H. HADDAR, Identifying defects in an unknown background using differential measurements, Inverse Probl. Imaging, 9 (2015), pp. 625-643. (Cited on pp. 35, 42, 66, 68)
    • (2015) Inverse Probl. Imaging , vol.9 , pp. 625-643
    • Audibert, L.1    Girard, A.2    Haddar, H.3
  • 7
    • 84894550883 scopus 로고    scopus 로고
    • A generalized formulation of the linear sampling method with exact characterization of targets in terms of far field measurements
    • (Cited on pp. ix, 35, 42, 46, 49, 65, 66, 67)
    • L. AUDIBERT AND H. HADDAR, A generalized formulation of the linear sampling method with exact characterization of targets in terms of far field measurements, Inverse Problems, 30:035011 (2014). (Cited on pp. ix, 35, 42, 46, 49, 65, 66, 67)
    • (2014) Inverse Problems , vol.30 , pp. 035011
    • Audibert, L.1    Haddar, H.2
  • 8
    • 0040200809 scopus 로고
    • Explicit solution of the inverse problem for a vibrating string
    • (Cited on p. 174)
    • V. BARCIION, Explicit solution of the inverse problem for a vibrating string, J. Math. Anal. Appl., 93 (1983), pp. 222-234. (Cited on p. 174)
    • (1983) J. Math. Anal. Appl. , vol.93 , pp. 222-234
    • Barciion, V.1
  • 10
    • 84884645336 scopus 로고    scopus 로고
    • Strongly oscillating singularities for the interior transmission eigenvalue problem
    • (Cited on pp.97, 123)
    • A.-S. BONNET-BENDHIA AND L. CHESNEL, Strongly oscillating singularities for the interior transmission eigenvalue problem, Inverse Problems, 29:104004 (2013). (Cited on pp.97, 123)
    • (2013) Inverse Problems , vol.29 , pp. 104004
    • Bonnet-Bendhia, A.-S.1    Chesnel, L.2
  • 11
    • 84899738793 scopus 로고    scopus 로고
    • 1-coercivity for the Maxwell problem with sign-changing coefficients
    • (Cited on p. 123)
    • A.-S. BONNET-BEN DHIA, L. CHESNEL, AND P. CIARLET, JR., 1-coercivity for the Maxwell problem with sign-changing coefficients, Comm. Partial Differential Equations, 39 (2014), pp. 1007-1031. (Cited on p. 123)
    • (2014) Comm. Partial Differential Equations , vol.39 , pp. 1007-1031
    • Bonnet-Ben Dhia, A.-S.1    Chesnel, L.2    Ciarlet, P.3
  • 12
    • 79959494396 scopus 로고    scopus 로고
    • On the use of T-coercivity to study the interior transmission eigenvalue problem
    • (Cited on pp. 80, 118)
    • A.-S. BONNET-BENDHIA, L. CHESNEL, AND H. HADDAR, On the use of T-coercivity to study the interior transmission eigenvalue problem, C. R. Math. Acad. Sci. Paris, 349 (2011), pp. 647-651. (Cited on pp. 80, 118)
    • (2011) C. R. Math. Acad. Sci. Paris , Issue.349 , pp. 647-651
    • Bonnet-Bendhia, A.-S.1    Chesnel, L.2    Haddar, H.3
  • 13
    • 84946176772 scopus 로고    scopus 로고
    • On the identification of defects in a periodic waveguide from far field data
    • (Cited on pp. 35, 36)
    • L. BOURGEOIS AND S. FLISS, On the identification of defects in a periodic waveguide from far field data, Inverse Problems, 30:095004 (2014). (Cited on pp. 35, 36)
    • (2014) Inverse Problems , vol.30 , pp. 095004
    • Bourgeois, L.1    Fliss, S.2
  • 16
    • 78649801117 scopus 로고    scopus 로고
    • The interior transmission eigenvalue problem
    • (Cited on pp. 114, 142, 143, 182)
    • F. CAKONI, D. COLTON, AND D. GINTIDES, The interior transmission eigenvalue problem, SIAMJ. Math. Anal., 42 (2010), pp. 2912-2921. (Cited on pp. 114, 142, 143, 182)
    • (2010) SIAMJ. Math. Anal. , vol.42 , pp. 2912-2921
    • Cakoni, F.1    Colton, D.2    Gintides, D.3
  • 17
    • 0037106174 scopus 로고    scopus 로고
    • The linear sampling method for anisotropic media
    • (Cited on pp. 80, 110)
    • F. CAKONI, D. COLTON, AND H. HADDAR, The linear sampling method for anisotropic media, J. Comput. Appl. Math., 146 (2002), pp. 285-299. (Cited on pp. 80, 110)
    • (2002) J. Comput. Appl. Math. , vol.146 , pp. 285-299
    • Cakoni, F.1    Colton, D.2    Haddar, H.3
  • 18
    • 67651213840 scopus 로고    scopus 로고
    • The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data
    • (Cited on p. 166)
    • -, The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data, J. Integral Equations Appl., 21 (2009), pp. 203-227. (Cited on p. 166)
    • (2009) J. Integral Equations Appl. , vol.21 , pp. 203-227
    • Cakoni, F.1    Colton, D.2    Haddar, H.3
  • 19
    • 77954406522 scopus 로고    scopus 로고
    • The interior transmission problem for regions with cavities
    • (Cited on pp. 84, 90, 138)
    • -, The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42 (2010), pp. 145-162. (Cited on pp. 84, 90, 138)
    • (2010) SIAM J. Math. Anal. , vol.42 , pp. 145-162
    • Cakoni, F.1    Colton, D.2    Haddar, H.3
  • 20
    • 77949491426 scopus 로고    scopus 로고
    • On the determination of Dirichlet or transmission eigenvalues from far field data
    • (Cited on pp. 114, 165, 166)
    • -, On the determination of Dirichlet or transmission eigenvalues from far field data, C.R. Math. Acad. Sci. Paris, 348 (2010), pp. 379-383. (Cited on pp. 114, 165, 166)
    • (2010) C.R. Math. Acad. Sci. Paris , vol.348 , pp. 379-383
    • Cakoni, F.1    Colton, D.2    Haddar, H.3
  • 21
    • 84858722954 scopus 로고    scopus 로고
    • The interior transmission eigenvalue problem for absorbing media
    • (Cited on pp. 126, 146)
    • -, The interior transmission eigenvalue problem for absorbing media, Inverse Problems, 28:045005 (2012). (Cited on pp. 126, 146)
    • (2012) Inverse Problems , vol.28 , pp. 045005
    • Cakoni, F.1    Colton, D.2    Haddar, H.3
  • 22
    • 84897422873 scopus 로고    scopus 로고
    • The inverse scattering problem for a penetrable cavity with internal measurements
    • vol. 615 of Con-temp. Math., American Mathematical Society, Providence, RI,. (Cited on p. 104)
    • F. CAKONI, D. COLTON, AND S. MENG, The inverse scattering problem for a penetrable cavity with internal measurements, in Inverse Problems and Applications, vol. 615 of Con-temp. Math., American Mathematical Society, Providence, RI, 2014, pp. 71-88. (Cited on p. 104)
    • (2014) Inverse Problems and Applications , pp. 71-88
    • Cakoni, F.1    Colton, D.2    Meng, S.3
  • 23
    • 33947388035 scopus 로고    scopus 로고
    • On the use of transmission eigenvalues to estimate the index of refraction from far field data
    • (Cited on p. 166)
    • F. CAKONI, D. COLTON, AND P. MONK, On the use of transmission eigenvalues to estimate the index of refraction from far field data, Inverse Problems, 23 (2007), pp. 507-522. (Cited on p. 166)
    • (2007) Inverse Problems , vol.23 , pp. 507-522
    • Cakoni, F.1    Colton, D.2    Monk, P.3
  • 25
    • 77951987363 scopus 로고    scopus 로고
    • The inverse electromagnetic scattering problem for anisotropic media
    • (Cited on p. 167)
    • F. CAKONI, D. COLTON, P. MONK, AND J. SUN, The inverse electromagnetic scattering problem for anisotropic media, Inverse Problems, 26:074004 (2010). (Cited on p. 167)
    • (2010) Inverse Problems , vol.26 , pp. 074004
    • Cakoni, F.1    Colton, D.2    Monk, P.3    Sun, J.4
  • 26
    • 84866459815 scopus 로고    scopus 로고
    • Transmission eigenvalues for inhomo-geneous media containing obstacles
    • (Cited on p. 90)
    • F. CAKONI, A. COSSONNIERE, AND H. HADDAR, Transmission eigenvalues for inhomo-geneous media containing obstacles, Inverse Probl. Imaging, 6 (2012), pp. 373-398. (Cited on p. 90)
    • (2012) Inverse Probl. Imaging , vol.6 , pp. 373-398
    • Cakoni, F.1    Cossonniere, A.2    Haddar, H.3
  • 27
    • 77950574432 scopus 로고    scopus 로고
    • The existence of an infinite discrete set of transmission eigenvalues
    • (Cited on pp. ix, 82, 125, 132)
    • F. CAKONI, D. GlNTIDES, AND H. HADDAR, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), pp. 237-255. (Cited on pp. ix, 82, 125, 132)
    • (2010) SIAM J. Math. Anal. , vol.42 , pp. 237-255
    • Cakoni, F.1    Glntides, D.2    Haddar, H.3
  • 28
    • 33845402170 scopus 로고    scopus 로고
    • Interior transmission problem for anisotropic media
    • Springer, Berlin, 2003. (Cited on pp. 80, 110, 112)
    • F. CAKONI AND H. HADDAR, Interior transmission problem for anisotropic media, in Mathematical and Numerical Aspects of Wave Propagation, 2003, Springer, Berlin, 2003, pp. 613-618. (Cited on pp. 80, 110, 112)
    • (2003) Mathematical and Numerical Aspects of Wave Propagation , pp. 613-618
    • Cakoni, F.1    Haddar, H.2
  • 29
    • 67651235537 scopus 로고    scopus 로고
    • On the existence of transmission eigenvalues in an inhomogeneous medium
    • (Cited on pp. 82, 114, 126, 133)
    • -, On the existence of transmission eigenvalues in an inhomogeneous medium, Appl. Anal., 88 (2009), pp. 475-493. (Cited on pp. 82, 114, 126, 133)
    • (2009) Appl. Anal. , vol.88 , pp. 475-493
    • Cakoni, F.1    Haddar, H.2
  • 30
    • 84885380611 scopus 로고    scopus 로고
    • Transmission eigenvalues in inverse scattering theory
    • vol. 60 of Math. Sci. Res. Inst. Publ., Cambridge University Press, Cambridge, UK,. (Cited on p. 82)
    • -, Transmission eigenvalues in inverse scattering theory, in Inverse Problems and Applications: Inside Out. II, vol. 60 of Math. Sci. Res. Inst. Publ., Cambridge University Press, Cambridge, UK, 2013, pp. 529-580. (Cited on p. 82)
    • (2013) Inverse Problems and Applications: Inside Out. II , pp. 529-580
    • Cakoni, F.1    Haddar, H.2
  • 31
    • 84957891529 scopus 로고    scopus 로고
    • Boundary integral equations for the transmission eigenvalue problem for Maxwell's equations
    • (Cited on p. 123)
    • F. CAKONI, H. HADDAR, AND S. MENG, Boundary integral equations for the transmission eigenvalue problem for Maxwell's equations, J. Integral Equations Appl., 27 (2015), pp. 375-406. (Cited on p. 123)
    • (2015) J. Integral Equations Appl. , vol.27 , pp. 375-406
    • Cakoni, F.1    Haddar, H.2    Meng, S.3
  • 32
    • 77954399565 scopus 로고    scopus 로고
    • On the interior transmission eigenvalue problem
    • (Cited on pp. 126, 154, 156, 161)
    • F. CAKONI AND A. KlRSCH, On the interior transmission eigenvalue problem, Int. J. Comput. Sci. Math., 3 (2010), pp. 142-167. (Cited on pp. 126, 154, 156, 161)
    • (2010) Int. J. Comput. Sci. Math. , vol.3 , pp. 142-167
    • Cakoni, F.1    Klrsch, A.2
  • 33
    • 85006031080 scopus 로고    scopus 로고
    • A boundary integral equation method for the transmission eigenvalue problem
    • to appear. (Cited on p. 108)
    • F. CAKONI AND R. KRESS, A boundary integral equation method for the transmission eigenvalue problem, Appl. Anal., to appear (2016). (Cited on p. 108)
    • (2016) Appl. Anal.
    • Cakoni, F.1    Kress, R.2
  • 34
    • 0002713385 scopus 로고
    • On an inverse boundary value problem, in seminar on numerical analysis and its applications to continuum physics
    • Rio de Janeiro,. (Cited on p. 16)
    • A. CALDERON, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Sociedade Brasileira de Matematica, Rio de Janeiro, 1980, pp. 65-73. (Cited on p. 16)
    • (1980) Sociedade Brasileira de Matematica , pp. 65-73
    • Calderon, A.1
  • 35
    • 1842683272 scopus 로고    scopus 로고
    • Nonlinear eigenvalues and analytic hy-poellipticity
    • (Cited on p. 144)
    • S. CHANILLO, B. HELFFER, AND A. LAPTEV, Nonlinear eigenvalues and analytic hy-poellipticity, J. Funct. Anal., 209 (2004), pp. 425-443. (Cited on p. 144)
    • (2004) J. Funct. Anal. , vol.209 , pp. 425-443
    • Chanillo, S.1    Helffer, B.2    Laptev, A.3
  • 37
    • 0346946901 scopus 로고    scopus 로고
    • Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems
    • (Cited on p. 41)
    • F. COLLINO, M. FARES, AND H. HADDAR, Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems, Inverse Problems, 19 (2003), pp. 1279-1298. (Cited on p. 41)
    • (2003) Inverse Problems , vol.19 , pp. 1279-1298
    • Collino, F.1    Fares, M.2    Haddar, H.3
  • 38
    • 0347577839 scopus 로고    scopus 로고
    • The linear sampling method in inverse electromagnetic scattering theory
    • (Cited on pp. 35, 36, 41)
    • D. COLTON, H. HADDAR, AND M. PlANA, The linear sampling method in inverse electromagnetic scattering theory, Inverse Problems, 19 (2003), pp. S105-S137. (Cited on pp. 35, 36, 41)
    • (2003) Inverse Problems , vol.19 , pp. S105-S137
    • Colton, D.1    Haddar, H.2    Plana, M.3
  • 39
    • 0000978411 scopus 로고    scopus 로고
    • A simple method for solving inverse scattering problems in the resonance region
    • (Cited on pp. ix, 35, 36)
    • D. CoLTON AND A. KlRSCH, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12 (1996), pp. 383-393. (Cited on pp. ix, 35, 36)
    • (1996) Inverse Problems , vol.12 , pp. 383-393
    • Colton, D.1    Klrsch, A.2
  • 40
    • 0012355575 scopus 로고
    • Far-field patterns for acoustic waves in an inhomogeneous medium
    • (Cited on p. 144)
    • D. COLTON, A. KlRSCH, AND L. PAlVARINTA, Far-field patterns for acoustic waves in an inhomogeneous medium, SIAM J. Math. Anal., 20 (1989), pp. 1472-1483. (Cited on p. 144)
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 1472-1483
    • Colton, D.1    Klrsch, A.2    Palvarinta, L.3
  • 41
    • 21844519224 scopus 로고
    • Eigenvalues of the far field operator and inverse scattering theory
    • (Cited on p. 13)
    • D. COLTON AND R. KRESS, Eigenvalues of the far field operator and inverse scattering theory, SIAM J. Math. Anal., 26 (1995), pp. 601-615. (Cited on p. 13)
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 601-615
    • Colton, D.1    Kress, R.2
  • 42
    • 0003584504 scopus 로고    scopus 로고
    • Springer, New York, 3rd ed. (Cited on pp. ix, 3, 8, 11, 13, 17, 19, 21, 24, 29, 38, 97, 104, 123, 130, 131, 148, 155, 174,)
    • -, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, New York, 3rd ed., 2013. (Cited on pp. ix, 3, 8, 11, 13, 17, 19, 21, 24, 29, 38, 97, 104, 123, 130, 131, 148, 155, 174, 182)
    • (2013) Inverse Acoustic and Electromagnetic Scattering Theory , pp. 182
    • Colton, D.1    Kress, R.2
  • 43
    • 84884639329 scopus 로고    scopus 로고
    • Complex eigenvalues and the inverse spectral problem for transmission eigenvalues
    • (Cited on p. 176)
    • D. CoLTON AND Y. J. LEUNG, Complex eigenvalues and the inverse spectral problem for transmission eigenvalues, Inverse Problems, 29:104008 (2013). (Cited on p. 176)
    • (2013) Inverse Problems , vol.29 , pp. 104008
    • Colton, D.1    Leung, Y.J.2
  • 44
    • 84923170135 scopus 로고    scopus 로고
    • Distribution of complex transmission eigenvalues for spherically stratified media
    • (Cited on pp. 130, 180)
    • D. COLTON, Y. J. LEUNG, AND S. MENG, Distribution of complex transmission eigenvalues for spherically stratified media, Inverse Problems, 31:035006 (2015). (Cited on pp. 130, 180)
    • (2015) Inverse Problems , vol.31 , pp. 035006
    • Colton, D.1    Leung, Y.J.2    Meng, S.3
  • 45
    • 84907646354 scopus 로고    scopus 로고
    • Spectral properties ofthe exterior transmission eigenvalue problem
    • (Cited on p. 104)
    • D. Co ETON AND S. MENG, Spectral properties ofthe exterior transmission eigenvalue problem, Inverse Problems, 30:105010 (2014). (Cited on p. 104)
    • (2014) Inverse Problems , vol.30 , pp. 105010
    • Co Eton, D.1    Meng, S.2
  • 46
    • 0343683857 scopus 로고
    • The inverse scattering problem for acoustic waves in an inhomogeneous medium
    • (Cited on pp. ix, 15, 16)
    • D. COLTON AND P. MONK, The inverse scattering problem for acoustic waves in an inhomogeneous medium, Quart. J. Mech. Appl. Math., 41 (1988), pp. 97-125. (Cited on pp. ix, 15, 16)
    • (1988) Quart. J. Mech. Appl. Math. , vol.41 , pp. 97-125
    • Colton, D.1    Monk, P.2
  • 47
    • 0039768609 scopus 로고    scopus 로고
    • Transmission eigenvalues and a problem of Hans Lewy
    • (Cited on p. 144)
    • D. COLTON AND L. PAlVARINTA, Transmission eigenvalues and a problem ofHansLewy, J. Comput. Appl. Math., 117 (2000), pp. 91-104. (Cited on p. 144)
    • (2000) J. Comput. Appl. Math. , vol.117 , pp. 91-104
    • Colton, D.1    Palvarinta, L.2
  • 48
    • 85029834942 scopus 로고    scopus 로고
    • The interior transmission problem
    • (Cited on pp. 131, 155, 174)
    • D. COLTON, L. PAlVARlNTA, AND J. SYLVESTER, The interior transmission problem, Inverse Probl. Imaging, 1 (2007), pp. 13-28. (Cited on pp. 131, 155, 174)
    • (2007) Inverse Probl. Imaging , vol.1 , pp. 13-28
    • Colton, D.1    Palvarlnta, L.2    Sylvester, J.3
  • 49
    • 3343011404 scopus 로고    scopus 로고
    • A simple method using Morozov's discrepancy principle for solving inverse scattering problems
    • (Cited on pp. 35, 36, 42)
    • D. COLTON, M. PlANA, AND R. PoTTHAST, A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, 13 (1997), pp. 1477-1493. (Cited on pp. 35, 36, 42)
    • (1997) Inverse Problems , vol.13 , pp. 1477-1493
    • Colton, D.1    Plana, M.2    Potthast, R.3
  • 51
    • 80052742652 scopus 로고    scopus 로고
    • The electromagnetic interior transmission problem for regions with cavities
    • (Cited on pp. 84, 123)
    • A. COSSONNIERE AND H. HADDAR, The electromagnetic interior transmission problem for regions with cavities, SIAM J. Math. Anal., 43 (2011), pp. 1698-1715. (Cited on pp. 84, 123)
    • (2011) SIAM J. Math. Anal. , vol.43 , pp. 1698-1715
    • Cossonniere, A.1    Haddar, H.2
  • 52
    • 84885378013 scopus 로고    scopus 로고
    • Surface integral formulation of the interior transmission problem
    • (Cited on pp. 80, 97, 99, 101, 108)
    • -, Surface integral formulation of the interior transmission problem, J. Integral Equations Appl, 25 (2013), pp. 341-376. (Cited on pp. 80, 97, 99, 101, 108)
    • (2013) J. Integral Equations Appl , vol.25 , pp. 341-376
    • Cossonniere, A.1    Haddar, H.2
  • 53
    • 84884632148 scopus 로고    scopus 로고
    • Transmission eigenvalues for Maxwell's equations in isotropic absorbing media with frequency-dependent electrical parameters
    • (Cited on pp. 126, 146)
    • F. DELBARY, Transmission eigenvalues for Maxwell's equations in isotropic absorbing media with frequency-dependent electrical parameters, Inverse Problems, 29:104005 (2013). (Cited on pp. 126, 146)
    • (2013) Inverse Problems , vol.29 , pp. 104005
    • Delbary, F.1
  • 57
    • 84884646915 scopus 로고    scopus 로고
    • Transmission eigenvalues and thermoacoustic tomography
    • (Cited on p. 144)
    • D. FINCH AND K. S. HlCKMANN, Transmission eigenvalues and thermoacoustic tomography, Inverse Problems, 29:104016 (2013). (Cited on p. 144)
    • (2013) Inverse Problems , vol.29 , pp. 104016
    • Finch, D.1    Hlckmann, K.S.2
  • 59
    • 84860285815 scopus 로고    scopus 로고
    • Computing estimates of material properties from transmission eigenvalues
    • (Cited on pp. 166, 167, 168)
    • G. GlORGI AND H. HADDAR, Computing estimates of material properties from transmission eigenvalues, Inverse Problems, 28:055009 (2012). (Cited on pp. 166, 167, 168)
    • (2012) Inverse Problems , vol.28 , pp. 055009
    • Glorgi, G.1    Haddar, H.2
  • 60
    • 0001185788 scopus 로고    scopus 로고
    • An inverse problem for the Helmholtz equation
    • (Cited on p. 31)
    • F. GYLYS-COLWELL, An inverse problem for the Helmholtz equation, Inverse Problems, 12 (1996), pp. 139-156. (Cited on p. 31)
    • (1996) Inverse Problems , vol.12 , pp. 139-156
    • Gylys-Colwell, F.1
  • 61
    • 0033896110 scopus 로고    scopus 로고
    • On the uniqueness of the shape of a penetrable, anisotropic obstacle
    • (Cited on p. 31)
    • P. HAHNER, On the uniqueness of the shape of a penetrable, anisotropic obstacle, J. Comput. Appl. Math., 116 (2000), pp. 167-180. (Cited on p. 31)
    • (2000) J. Comput. Appl. Math. , vol.116 , pp. 167-180
    • Hahner, P.1
  • 62
    • 84894576135 scopus 로고    scopus 로고
    • Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids
    • (Cited on pp. 161, 167)
    • I. HARRIS, F. CAKONI, AND J. SUN, Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids, Inverse Problems, 30:035016 (2014). (Cited on pp. 161, 167)
    • (2014) Inverse Problems , vol.30 , pp. 035016
    • Harris, I.1    Cakoni, F.2    Sun, J.3
  • 63
    • 84866036452 scopus 로고    scopus 로고
    • Interior transmission eigenvalue problem with refractive index having C2-transition to the background medium
    • (Cited on p. 144)
    • K. S. HlCKMANN, Interior transmission eigenvalue problem with refractive index having C2-transition to the background medium, Appl. Anal., 91 (2012), pp. 1675-1690. (Cited on p. 144)
    • (2012) Appl. Anal. , vol.91 , pp. 1675-1690
    • Hlckmann, K.S.1
  • 64
    • 79955544674 scopus 로고    scopus 로고
    • The interior transmission problem and bounds on transmission eigenvalues
    • (Cited on p. 143)
    • M. HITRIK, K. KRUPCHYK, P. OLA, AND L. PAIVARINTA, The interior transmission problem and bounds on transmission eigenvalues, Math. Res. Lett., 18 (2011), pp. 279-293. (Cited on p. 143)
    • (2011) Math. Res. Lett. , vol.18 , pp. 279-293
    • Hitrik, M.1    Krupchyk, K.2    Ola, P.3    Paivarinta, L.4
  • 67
    • 84990557331 scopus 로고
    • On uniqueness of recovery of a discontinuous conductivity coefficient
    • (Cited on p. 31)
    • V. ISAKOV, On uniqueness of recovery of a discontinuous conductivity coefficient, Comm. Pure Appl. Math., 41 (1988), pp. 865-877. (Cited on p. 31)
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 865-877
    • Isakov, V.1
  • 69
    • 84884171977 scopus 로고    scopus 로고
    • A multi-level method for transmission eigenvalues of anisotropic media
    • (Cited on p. 164)
    • X. JI AND J. SUN, A multi-level method for transmission eigenvalues of anisotropic media, J. Comput. Phys., 255 (2013), pp. 422-435. (Cited on p. 164)
    • (2013) J. Comput. Phys. , vol.255 , pp. 422-435
    • Ji, X.1    Sun, J.2
  • 70
    • 84863163473 scopus 로고    scopus 로고
    • Algorithm 922: A mixed finite element method for Helmholtz transmission eigenvalues
    • (Cited on p. 164)
    • X. JI, J. SUN, AND T. TURNER, Algorithm 922: A mixed finite element method for Helmholtz transmission eigenvalues, ACM Trans. Math. Software, 38 (2012), pp. Art. ID 29, 8. (Cited on p. 164)
    • (2012) ACM Trans. Math. Software , vol.38
    • Ji, X.1    Sun, J.2    Turner, T.3
  • 71
    • 84978847075 scopus 로고    scopus 로고
    • Computing interior eigenvalues of domains from far fields
    • (Cited on p. 172)
    • Z. JIANG AND A. LECHLEITER, Computing interior eigenvalues of domains from far fields, IMA J. Numer. Anal, 36 (2016), pp. 1452-1476. (Cited on p. 172)
    • (2016) IMA J. Numer. Anal , vol.36 , pp. 1452-1476
    • Jiang, Z.1    Lechleiter, A.2
  • 73
    • 0008426112 scopus 로고
    • Thedenseness of the far fieldpattern for the transmission problem
    • (Cited on pp. ix, 15, 16)
    • A. KIRSCH, Thedenseness of the far fieldpattern for the transmission problem, IMA J. Appl. Math., 37 (1986), pp. 213-225. (Cited on pp. ix, 15, 16)
    • (1986) IMA J. Appl. Math. , vol.37 , pp. 213-225
    • Kirsch, A.1
  • 74
    • 0001119601 scopus 로고    scopus 로고
    • Factorization of the far field operator for the inhomogeneous medium case and an application to inverse scattering theory
    • (Cited on pp. ix, 20, 36, 54, 58)
    • -, Factorization of the far field operator for the inhomogeneous medium case and an application to inverse scattering theory, Inverse Problems, 15 (1999), pp. 413-429. (Cited on pp. ix, 20, 36, 54, 58)
    • (1999) Inverse Problems , vol.15 , pp. 413-429
    • Kirsch, A.1
  • 75
    • 67651210758 scopus 로고    scopus 로고
    • On the existence of transmission eigenvalues
    • (Cited on p. 156)
    • -, On the existence of transmission eigenvalues, Inverse Probl. Imaging, 3 (2009), pp. 155-172. (Cited on p. 156)
    • (2009) Inverse Probl. Imaging , vol.3 , pp. 155-172
    • Kirsch, A.1
  • 77
    • 84960405958 scopus 로고    scopus 로고
    • A note on Sylvester's proof of discreteness of interior transmission eigenvalues
    • Cited on pp. 79, 90, 91
    • -, A note on Sylvester's proof of discreteness of interior transmission eigenvalues, C. R. Math. Acad. Sci. Paris, 354 (2016), pp. 377-382. (Cited on pp. 79, 90, 91)
    • (2016) C. R. Math. Acad. Sci. Paris , vol.354 , pp. 377-382
    • Kirsch, A.1
  • 79
    • 84884626709 scopus 로고    scopus 로고
    • The inside-outside duality for scattering problems by inhomogeneous media
    • (Cited on pp. 165, 172)
    • A. KIRSCH AND A. LECHLEITER, The inside-outside duality for scattering problems by inhomogeneous media, Inverse Problems, 29:104011 (2013). (Cited on pp. 165, 172)
    • (2013) Inverse Problems , vol.29 , pp. 104011
    • Kirsch, A.1    Lechleiter, A.2
  • 80
    • 84884655216 scopus 로고    scopus 로고
    • A numerical method to compute interior transmission eigenvalues
    • (Cited on p. 164)
    • A. KLEEFELD, A numerical method to compute interior transmission eigenvalues, Inverse Problems, 29:104012 (2013). (Cited on p. 164)
    • (2013) Inverse Problems , vol.29 , pp. 104012
    • Kleefeld, A.1
  • 81
    • 0003569751 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK, Cited on pp. 179, 180
    • P. KOOSIS, The Logarithmic Integral I, Cambridge University Press, Cambridge, UK, 1998. (Cited on pp. 179, 180)
    • (1998) The Logarithmic Integral i
    • Koosis, P.1
  • 82
    • 0003449635 scopus 로고    scopus 로고
    • Springer, New York, 3rd ed.,. (Cited on pp. 20, 24, 98, 99)
    • R. KRESS, Linear Integral Equations, Springer, New York, 3rd ed., 2014. (Cited on pp. 20, 24, 98, 99)
    • (2014) Linear Integral Equations
    • Kress, R.1
  • 83
    • 84867263183 scopus 로고    scopus 로고
    • Bounds on positive interior transmission eigenvalues
    • (Cited on pp. 123, 126, 164)
    • E. LAKSHTANOV AND B. VAINBERG, Bounds on positive interior transmission eigenvalues, Inverse Problems, 28:105005 (2012). (Cited on pp. 123, 126, 164)
    • (2012) Inverse Problems , vol.28 , pp. 105005
    • Lakshtanov, E.1    Vainberg, B.2
  • 84
    • 84861374501 scopus 로고    scopus 로고
    • Ellipticity in the interior transmission problem in anisotropic media
    • (Cited on pp. 123, 164)
    • -, Ellipticity in the interior transmission problem in anisotropic media, SIAM J. Math. Anal., 44 (2012), pp. 1165-1174. (Cited on pp. 123, 164)
    • (2012) SIAM J. Math. Anal. , vol.44 , pp. 1165-1174
    • Lakshtanov, E.1    Vainberg, B.2
  • 85
    • 84884599414 scopus 로고    scopus 로고
    • Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
    • (Cited on pp. 79, 123, 145, 164)
    • -, Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem, Inverse Problems, 29:104003 (2013). (Cited on pp. 79, 123, 145, 164)
    • (2013) Inverse Problems , vol.29 , pp. 104003
    • Lakshtanov, E.1    Vainberg, B.2
  • 86
    • 84905660318 scopus 로고    scopus 로고
    • Weyl type bound on positive interior transmission eigenvalues
    • (Cited on pp. 80, 123, 126, 164)
    • -, Weyl type bound on positive interior transmission eigenvalues, Comm. Partial Differential Equations, 39 (2014), pp. 1729-1740. (Cited on pp. 80, 123, 126, 164)
    • (2014) Comm. Partial Differential Equations , vol.39 , pp. 1729-1740
    • Lakshtanov, E.1    Vainberg, B.2
  • 87
    • 84940863301 scopus 로고    scopus 로고
    • Sharp Weyl law for signed counting function of positive interior transmission eigenvalues
    • (Cited on p. 145)
    • -, Sharp Weyl law for signed counting function of positive interior transmission eigenvalues, SIAM J. Math. Anal., 47 (2015), pp. 3212-3234. (Cited on p. 145)
    • (2015) SIAM J. Math. Anal. , vol.47 , pp. 3212-3234
    • Lakshtanov, E.1    Vainberg, B.2
  • 88
    • 0141995399 scopus 로고    scopus 로고
    • Wiley-Interscience, New York, Cited on pp. 127, 129
    • P. D. LAX, Functional Analysis, Wiley-Interscience, New York, 2002. (Cited on pp. 127, 129)
    • (2002) Functional Analysis
    • Lax, P.D.1
  • 89
    • 70350275150 scopus 로고    scopus 로고
    • The factorization method is independent of transmission eigenvalues
    • (Cited on p. 58)
    • A. LECHLEITER, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging, 3 (2009), pp. 123-138. (Cited on p. 58)
    • (2009) Inverse Probl. Imaging , vol.3 , pp. 123-138
    • Lechleiter, A.1
  • 90
    • 80051887825 scopus 로고    scopus 로고
    • Explicit characterization of the support of non-linear inclusions
    • (Cited on p. 54)
    • -, Explicit characterization of the support of non-linear inclusions, Inverse Probl. Imaging, 5 (2011), pp. 675-694. (Cited on p. 54)
    • (2011) Inverse Probl. Imaging , vol.5 , pp. 675-694
    • Lechleiter, A.1
  • 91
    • 84897436391 scopus 로고    scopus 로고
    • Analytical characterization and numerical approximation of interior eigenvalues for impenetrable scatterers from far fields
    • (Cited on p. 172)
    • A. LECHLEITER AND S. PETERS, Analytical characterization and numerical approximation of interior eigenvalues for impenetrable scatterers from far fields, Inverse Problems, 30:045006 (2014). (Cited on p. 172)
    • (2014) Inverse Problems , vol.30 , pp. 045006
    • Lechleiter, A.1    Peters, S.2
  • 92
    • 84863855777 scopus 로고    scopus 로고
    • Complex transmission eigenvalues for spherically stratified media
    • (Cited on p. 174)
    • Y. J. LEUNG AND D. COLTON, Complex transmission eigenvalues for spherically stratified media, Inverse Problems, 28:075005 (2012). (Cited on p. 174)
    • (2012) Inverse Problems , vol.28 , pp. 075005
    • Leung, Y.J.1    Colton, D.2
  • 96
    • 27144488534 scopus 로고
    • Zur mathematischen theorie elektromagnetischer schwingungen. abh. deutsch
    • (Cited on p. 11)
    • C. MÜLLER, Zur mathematischen theorie elektromagnetischer schwingungen. abh. deutsch, Akad. Wiss. Berlin, 3 (1945/46), pp. 5-56. (Cited on p. 11)
    • (1945) Akad. Wiss. Berlin , vol.3 , pp. 5-56
    • Müller, C.1
  • 97
    • 84980079173 scopus 로고
    • On the behavior of solutions of the differential equation δu = F(x, u) in the neighborhood of a point
    • (Cited on p. 11)
    • -, On the behavior of solutions of the differential equation δu = F(x, u) in the neighborhood of a point, Comm. Pure Appl. Math., 7 (1954), pp. 505-515. (Cited on p. 11)
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 505-515
    • Müller, C.1
  • 98
    • 0000426306 scopus 로고
    • Reconstructions from boundary measurements
    • (Cited on p. 17)
    • A. NACHMAN, Reconstructions from boundary measurements, Ann. of Math. (2), 128 (1988), pp. 531-576. (Cited on p. 17)
    • (1988) Ann. of Math. , vol.128 , Issue.2 , pp. 531-576
    • Nachman, A.1
  • 99
    • 35248871969 scopus 로고    scopus 로고
    • On imaging obstacles inside inho-mogeneous media
    • (Cited on p. 52)
    • A. I. NACHMAN, L. PÄIVÄRINTA, AND A. TEIRILA, On imaging obstacles inside inho-mogeneous media, J. Funct. Anal., 252 (2007), pp. 490-516. (Cited on p. 52)
    • (2007) J. Funct. Anal. , vol.252 , pp. 490-516
    • Nachman, A.I.1    Päivärinta, L.2    Teirila, A.3
  • 101
    • 34249973239 scopus 로고
    • A multidimensional inverse spectral problem for the equation -δψ + (v(x)- Eu(x))ψ = 0
    • (Cited on p. 17)
    • R.NOVIKOV, A multidimensional inverse spectral problem for the equation -δψ + (v(x)- Eu(x))ψ = 0, Funct. Anal. Appl., 22 (1988), pp. 263-272. (Cited on p. 17)
    • (1988) Funct. Anal. Appl. , vol.22 , pp. 263-272
    • Novikov, R.1
  • 102
    • 62649109684 scopus 로고    scopus 로고
    • Transmission eigenvalues
    • (Cited on pp. 82, 125, 129)
    • L. PAlVARlNTA AND J. SYLVESTER, Transmission eigenvalues, SIAM J. Math. Anal., 40 (2008), pp. 738-753. (Cited on pp. 82, 125, 129)
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 738-753
    • Palvarlnta, L.1    Sylvester, J.2
  • 103
    • 85006015897 scopus 로고    scopus 로고
    • Asymptotics of the number of the interior transmission eigenvalues
    • (Cited on p. 145)
    • V. PETKOV AND G. VODEV, Asymptotics of the number of the interior transmission eigenvalues, ]. Spectr. Theory, to appear (2016). (Cited on p. 145)
    • (2016) J. Spectr. Theory, to Appear
    • Petkov, V.1    Vodev, G.2
  • 104
    • 85006015896 scopus 로고    scopus 로고
    • Localization of transmission eigenvalues for a ball
    • (Cited on pp. 143, 175)
    • -, Localization of transmission eigenvalues for a ball, Inverse Probl. Imaging, to appear (2016). (Cited on pp. 143, 175)
    • (2016) Inverse Probl. Imaging, to Appear
    • Petkov, V.1    Vodev, G.2
  • 105
    • 84906903527 scopus 로고    scopus 로고
    • Weyl asymptotics of the transmission eigenvalues for a constant index of refraction
    • (Cited on p. 175)
    • H. PHAM AND P. STEFANOV, Weyl asymptotics of the transmission eigenvalues for a constant index of refraction, Inverse Probl. Imaging, 8 (2014), pp. 795-810. (Cited on p. 175)
    • (2014) Inverse Probl. Imaging , vol.8 , pp. 795-810
    • Pham, H.1    Stefanov, P.2
  • 106
    • 0001593593 scopus 로고
    • Recovery of the potential from fixed energy scattering data
    • (Cited on p. 17)
    • A. G. RAMM, Recovery of the potential from fixed energy scattering data, Inverse Problems, 4 (1988), pp. 877-886. (Cited on p. 17)
    • (1988) Inverse Problems , vol.4 , pp. 877-886
    • Ramm, A.G.1
  • 107
    • 0004057551 scopus 로고
    • Academic Press, New York, Cited on pp. 126, 129, 135, 137
    • M. REED AND B. SIMON, Functional Analysis, Academic Press, New York, 1980. (Cited on pp. 126, 129, 135, 137)
    • (1980) Functional Analysis
    • Reed, M.1    Simon, B.2
  • 108
    • 84884637935 scopus 로고    scopus 로고
    • Spectral analysis of the interior transmission eigenvalue problem
    • (Cited on pp. 126, 144, 145, 146)
    • L. ROBBIANO, Spectral analysis of the interior transmission eigenvalue problem, Inverse Problems, 29:104001 (2013). (Cited on pp. 126, 144, 145, 146)
    • (2013) Inverse Problems , vol.29 , pp. 104001
    • Robbiano, L.1
  • 109
    • 84968515990 scopus 로고
    • Reconstruction techniques for classical inverse Sturm-Liouvilleproblems
    • (Cited on p. 176)
    • W. RUNDELL AND P. SACKS, Reconstruction techniques for classical inverse Sturm-Liouvilleproblems, Math. Comp., 58 (1992), pp. 161-183. (Cited on p. 176)
    • (1992) Math. Comp. , vol.58 , pp. 161-183
    • Rundell, W.1    Sacks, P.2
  • 110
    • 0000423623 scopus 로고
    • The interior transmission problem and inverse scattering from inhomogeneous media
    • (Cited on pp. 38, 79, 82)
    • B. P. RYNNEANDB. D. SLEEMAN, The interior transmission problem and inverse scattering from inhomogeneous media, SIAM J. Math. Anal., 22 (1991), pp. 1755-1762. (Cited on pp. 38, 79, 82)
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1755-1762
    • Rynneandb, B.P.1    Sleeman, D.2
  • 111
    • 84860477457 scopus 로고    scopus 로고
    • Transmission eigenvalues for degenerate and singular cases
    • (Cited on p. 144)
    • V. SEROV AND J. SYLVESTER, Transmission eigenvalues for degenerate and singular cases, Inverse Problems, 28:065004 (2012). (Cited on p. 144)
    • (2012) Inverse Problems , vol.28 , pp. 065004
    • Serov, V.1    Sylvester, J.2
  • 113
    • 84858730794 scopus 로고    scopus 로고
    • Discreteness of transmission eigenvalues via upper triangular compact operators
    • (Cited on pp. 79, 90, 97, 108)
    • J. SYLVESTER, Discreteness of transmission eigenvalues via upper triangular compact operators, SIAM J. Math. Anal., 44 (2012), pp. 341-354. (Cited on pp. 79, 90, 97, 108)
    • (2012) SIAM J. Math. Anal. , vol.44 , pp. 341-354
    • Sylvester, J.1
  • 114
    • 84884633332 scopus 로고    scopus 로고
    • Transmission eigenvalues in one dimension
    • (Cited on p. 175)
    • -, Transmission eigenvalues in one dimension, Inverse Problems, 29:104009 (2013). (Cited on p. 175)
    • (2013) Inverse Problems , vol.29 , pp. 104009
    • Sylvester, J.1
  • 115
    • 0001110912 scopus 로고
    • I4 global uniqueness theorem for an inverse boundary value problem
    • (Cited on p. 17)
    • J. SYLVESTER AND G. UHLMANN, i4 global uniqueness theorem for an inverse boundary value problem, Ann. of Math. (2), 125 (1987), pp. 153-169. (Cited on p. 17)
    • (1987) Ann. of Math. , vol.125 , Issue.2 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2
  • 116
    • 84925537457 scopus 로고    scopus 로고
    • Transmission eigenvalue-free regions
    • (Cited on p. 143)
    • G. VODEV, Transmission eigenvalue-free regions, Comm. Math. Phys., 336 (2015), pp. 1141-1166. (Cited on p. 143)
    • (2015) Comm. Math. Phys. , vol.336 , pp. 1141-1166
    • Vodev, G.1
  • 117
    • 1642335531 scopus 로고    scopus 로고
    • Approximation by maxwell-herglotz-fields
    • (Cited on p. 87)
    • N. WECK, Approximation by Maxwell-Herglotz-fields, Math. Methods Appl. Sci., 27 (2004), pp. 603-621. (Cited on p. 87)
    • (2004) Math. Methods Appl. Sci. , vol.27 , pp. 603-621
    • Weck, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.