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Volumn 45, Issue 12, 2012, Pages

Remarks on interior transmission eigenvalues, Weyl formula and branching billiards

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EID: 84857945773     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/45/12/125202     Document Type: Article
Times cited : (26)

References (22)
  • 2
    • 0001772611 scopus 로고
    • Partial differential equations: Part VI. Elliptic operators on closed manifolds
    • Agranovich M S 1990 Partial differential equations: part VI. Elliptic operators on closed manifolds Encycl. Math. Sci. 63 1130 1994 (Engl. Transl.)
    • (1990) Encycl. Math. Sci. , vol.63 , pp. 1-130
    • Agranovich, M.S.1
  • 3
    • 0038870379 scopus 로고
    • Spectral asymptotics of non-self-adjoint elliptic systems of differential operators on bounded domains
    • Boimatov K Kh and Kostyuchenko A G 1990 Spectral asymptotics of non-self-adjoint elliptic systems of differential operators on bounded domains Mat. Sb. 1992 71:2 51731
    • (1990) Mat. Sb. , vol.712 , pp. 517-531
    • Boimatov, K.Kh.1    Kostyuchenko, A.G.2
  • 4
    • 77950574432 scopus 로고    scopus 로고
    • The existence of an infinite discrete set of transmission eigenvalues
    • Cakoni F, Gintides D and Haddar H 2010 The existence of an infinite discrete set of transmission eigenvalues SIAM J. Math. Anal. 42 23755
    • (2010) SIAM J. Math. Anal. , vol.42 , pp. 237-255
    • Cakoni, F.1    Gintides, D.2    Haddar, H.3
  • 5
    • 77954399565 scopus 로고    scopus 로고
    • On the interior transmission eigenvalue problem
    • Cakoni F and Kirsch A 2010 On the interior transmission eigenvalue problem Int. J. Comput. Sci. Math. 3 14267 (available at dl.acm.org/citation. cfm?id=1831377)
    • (2010) Int. J. Comput. Sci. Math. , vol.3 , pp. 142-167
    • Cakoni, F.1    Kirsch, A.2
  • 6
    • 0346540932 scopus 로고
    • Dense sets and far-field patterns in acoustic wave propagation
    • Colton D and Kirsch A 1984 Dense sets and far-field patterns in acoustic wave propagation SIAM J. Math. Anal. 15 996l006
    • (1984) SIAM J. Math. Anal. , vol.15
    • Colton, D.1    Kirsch, A.2
  • 7
    • 0343683857 scopus 로고
    • The inverse scattering problem for acoustic waves in an inhomogeneous medium
    • Colton D and Monk P 1988 The inverse scattering problem for acoustic waves in an inhomogeneous medium Q. J. Mech. Appl. Math. 41 97125
    • (1988) Q. J. Mech. Appl. Math. , vol.41 , pp. 97-125
    • Colton, D.1    Monk, P.2
  • 8
    • 0039768609 scopus 로고    scopus 로고
    • Transmission eigenvalues and a problem of Hans Lewy
    • Colton D and Paivarinta L 2000 Transmission eigenvalues and a problem of Hans Lewy J. Comput. Appl. Math. 117 91104
    • (2000) J. Comput. Appl. Math. , vol.117 , pp. 91-104
    • Colton, D.1    Paivarinta, L.2
  • 10
    • 18644373379 scopus 로고
    • Semiclassical quantization of chaotic billiards: A scattering theory approach
    • Doron E and Smilansky U 1992 Semiclassical quantization of chaotic billiards: a scattering theory approach Nonlinearity 5 105584
    • (1992) Nonlinearity , vol.5 , pp. 1055-1084
    • Doron, E.1    Smilansky, U.2
  • 11
  • 12
    • 0038427112 scopus 로고    scopus 로고
    • Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains
    • Eckmann J P and Pillet C-A 1997 Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains Helv. Phys. Acta 70 4465
    • (1997) Helv. Phys. Acta , vol.70 , pp. 44-65
    • Eckmann, J.P.1    Pillet, C.-A.2
  • 13
    • 0003301335 scopus 로고
    • Introduction to the theory of linear non-self-adjoint operators
    • Gohberg I and Krein M 1969 Introduction to the theory of linear non-self-adjoint operators Am. Math. Soc.
    • (1969) Am. Math. Soc.
    • Gohberg, I.1    Krein, M.2
  • 15
    • 84857988778 scopus 로고
    • On the spectral asymptotic expansion of the LaplaceBeltrami operator on manifolds with boundary
    • Ivrii V Y 1980 On the spectral asymptotic expansion of the LaplaceBeltrami operator on manifolds with boundary Sov. Math., Dokl. 21 3002 Zbl 0448.58024
    • (1980) Sov. Math., Dokl. , vol.21 , pp. 300-302
    • Ivrii, V.Y.1
  • 16
    • 0001241531 scopus 로고
    • Asymptotic behaviour of the scattering phase for exterior domains
    • Jensen A and Kato T 1978 Asymptotic behaviour of the scattering phase for exterior domains Commun. Part. Differ. Eqns 3 116595
    • (1978) Commun. Part. Differ. Eqns , vol.3 , pp. 1165-1195
    • Jensen, A.1    Kato, T.2
  • 17
    • 0008426112 scopus 로고
    • The denseness of the far-field patterns for the transmission problem
    • Kirsch A 1986 The denseness of the far-field patterns for the transmission problem IMA J. Appl. Math. 37 21325
    • (1986) IMA J. Appl. Math. , vol.37 , pp. 213-225
    • Kirsch, A.1
  • 19
    • 84972554773 scopus 로고
    • An analogue of Weyls theorem for unbounded domains: Part i
    • Majda A and Ralston J V 1978 An analogue of Weyls theorem for unbounded domains: part I Duke Math. J. 45 18396
    • (1978) Duke Math. J. , vol.45 , pp. 183-196
    • Majda, A.1    Ralston, J.V.2
  • 20
    • 0000179094 scopus 로고
    • Exact asymptotics of the spectrum of a boundary value problem, and periodic billiards
    • Safarov Yu G 1988 Exact asymptotics of the spectrum of a boundary value problem, and periodic billiards Izv. Akad. Nauk SSSR Ser. Mat. 52 123051 Zbl 0682.35082
    • (1988) Izv. Akad. Nauk SSSR Ser. Mat. , vol.52 , pp. 1230-1251
    • Safarov, Yu.G.1
  • 21
    • 84860477457 scopus 로고    scopus 로고
    • Transmission eigenvalues: Some degenerate and singular cases
    • Serov V and Sylvester J Transmission eigenvalues: some degenerate and singular cases Inverse Problems (at press)
    • Inverse Problems
    • Serov, V.1    Sylvester, J.2
  • 22
    • 0039379002 scopus 로고
    • Two-term asymptotics of the spectrum of a boundary-value problem under an interior reflection of general form
    • Vassilev D G 1984 Two-term asymptotics of the spectrum of a boundary-value problem under an interior reflection of general form Funkts. Anal. Prilozh. 18 113
    • (1984) Funkts. Anal. Prilozh. , vol.18 , pp. 1-13
    • Vassilev, D.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.