메뉴 건너뛰기




Volumn 126, Issue 6, 2004, Pages 1261-1313

Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in euclidean space

Author keywords

[No Author keywords available]

Indexed keywords


EID: 10844292800     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2004.0047     Document Type: Article
Times cited : (27)

References (39)
  • 1
    • 84990604696 scopus 로고
    • Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces
    • S. Agmon, Spectral theory of Schrödinger operators on Euclidean and non-Euclidean spaces, Comm. Pure Appl. Math. 39 Supplement (1986), S3-S16.
    • (1986) Comm. Pure Appl. Math. , vol.39 , Issue.SUPPL.
    • Agmon, S.1
  • 2
    • 84947680266 scopus 로고
    • To the reconstruction of a Riemannian manifold via its boundary spectral data (BC method)
    • M. I. Belishev and Y. V. Kurylev, To the reconstruction of a Riemannian manifold via its boundary spectral data (BC method). Comm. Partial Differential Equations 17 (1992), 767-804.
    • (1992) Comm. Partial Differential Equations , vol.17 , pp. 767-804
    • Belishev, M.I.1    Kurylev, Y.V.2
  • 3
    • 0001659228 scopus 로고    scopus 로고
    • Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
    • R. Brown and G. Uhlmann, Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions, Comm. Partial Differential Equations 22 (1997), 1009-1027.
    • (1997) Comm. Partial Differential Equations , vol.22 , pp. 1009-1027
    • Brown, R.1    Uhlmann, G.2
  • 4
    • 10844223395 scopus 로고    scopus 로고
    • The inverse scatering problem in two dimensions at fixed energy
    • G. Eskin, The inverse scatering problem in two dimensions at fixed energy, Comm. Partial Differential Equations 26 (2001), 1055-1090.
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 1055-1090
    • Eskin, G.1
  • 5
    • 21844485178 scopus 로고
    • Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy
    • G. Eskin and J. Ralston, Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy, Comm. Math. Phys. 173 (1995), 199-224.
    • (1995) Comm. Math. Phys. , vol.173 , pp. 199-224
    • Eskin, G.1    Ralston, J.2
  • 6
    • 0001649173 scopus 로고
    • Inverse problems of quantum scattering theory
    • L. D. Faddeev, Inverse problems of quantum scattering theory, J. Sov. Math. 5 (1976), 334-396.
    • (1976) J. Sov. Math. , vol.5 , pp. 334-396
    • Faddeev, L.D.1
  • 7
    • 84972579463 scopus 로고
    • Spectral analysis of second-order elliptic operators on non-compact manifolds
    • R. Froese and P. Hislop, Spectral analysis of second-order elliptic operators on non-compact manifolds, Duke Math. J. 58 (1989), 103-129.
    • (1989) Duke Math. J. , vol.58 , pp. 103-129
    • Froese, R.1    Hislop, P.2
  • 8
    • 51249168638 scopus 로고
    • The geometry and spectra of hyperbolic manifolds
    • P. D. Hislop, The geometry and spectra of hyperbolic manifolds, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 715-776.
    • (1994) Proc. Indian Acad. Sci. (Math. Sci.) , vol.104 , pp. 715-776
    • Hislop, P.D.1
  • 9
    • 0000709378 scopus 로고
    • Limiting absorption method and absolute continuity for the Schrödinger operator
    • T. Ikebe and Y. Saito, Limiting absorption method and absolute continuity for the Schrödinger operator, J. Math. Kyoto Univ. 12 (1972), 513-542.
    • (1972) J. Math. Kyoto Univ. , vol.12 , pp. 513-542
    • Ikebe, T.1    Saito, Y.2
  • 10
    • 0001311566 scopus 로고
    • Global uniqueness for a two-dimensional semilinear elliptic inverse problem
    • V. Isakov and A. Nachman, Global uniqueness for a two-dimensional semilinear elliptic inverse problem, Trans. Amer. Math. Soc. 347 (1995), 3375-3390.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 3375-3390
    • Isakov, V.1    Nachman, A.2
  • 11
    • 0040174316 scopus 로고
    • The inverse scattering at fixed energies in two dimensions
    • V. Isakov and Z. Sun, The inverse scattering at fixed energies in two dimensions, Indiana Univ. Math. J. 44 (1995), 883-896.
    • (1995) Indiana Univ. Math. J. , vol.44 , pp. 883-896
    • Isakov, V.1    Sun, Z.2
  • 12
    • 10844245310 scopus 로고    scopus 로고
    • Multi-dimensional inverse scattering theory
    • S. Saito et al., eds., Kluwer Academic Publishers, Dordrecht
    • H. Isozaki, Multi-dimensional inverse scattering theory. Analytic Extension Formulas and Their Applications (S. Saito et al., eds.), Kluwer Academic Publishers, Dordrecht, 2001, pp. 123-167.
    • (2001) Analytic Extension Formulas and Their Applications , pp. 123-167
    • Isozaki, H.1
  • 13
    • 10844280530 scopus 로고    scopus 로고
    • Inverse problems and hyperbolic manifolds
    • Inverse Problems and Spectral Theory Amer. Math. Soc., Providence, RI
    • _, Inverse problems and hyperbolic manifolds. Inverse Problems and Spectral Theory (H. Isozaki, ed.), Contemp. Math. vol. 348, Amer. Math. Soc., Providence, RI, 2004, pp. 181-197.
    • (2004) Contemp. Math. , vol.348 , pp. 181-197
    • Isozaki, H.1
  • 14
    • 4444285163 scopus 로고    scopus 로고
    • Hyperbolic geometry and local Dirichlet-Neumann map
    • H. Isozaki and G. Uhlmann, Hyperbolic geometry and local Dirichlet-Neumann map, Adv. Math. 188 (2004), 294-314.
    • (2004) Adv. Math. , vol.188 , pp. 294-314
    • Isozaki, H.1    Uhlmann, G.2
  • 15
    • 0001226256 scopus 로고
    • Unique continuation and absence of positive eigenvalues for Schrödinger operators
    • D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. 121 (1985), 463-494.
    • (1985) Ann. of Math. , vol.121 , pp. 463-494
    • Jerison, D.1    Kenig, C.E.2
  • 16
    • 0036600691 scopus 로고    scopus 로고
    • A uniqueness theorem for an inverse boundary value problem in two dimensions
    • H. Kang, A uniqueness theorem for an inverse boundary value problem in two dimensions, J. Math. Anal. Appl. 270 (2002), 291-302.
    • (2002) J. Math. Anal. Appl. , vol.270 , pp. 291-302
    • Kang, H.1
  • 17
    • 2442664239 scopus 로고    scopus 로고
    • Inverse problems for the Pauli Hamiltonian in two dimensions
    • H. Kang and G. Uhlmann, Inverse problems for the Pauli Hamiltonian in two dimensions, J. Fourier Anal. Appl. 10 (2004), 201-215.
    • (2004) J. Fourier Anal. Appl. , vol.10 , pp. 201-215
    • Kang, H.1    Uhlmann, G.2
  • 19
    • 0000451597 scopus 로고
    • The ∂̄-equation in the multi-dimensional inverse scattering problem
    • G. M. Khenkin and R. G. Novikov, The ∂̄-equation in the multi-dimensional inverse scattering problem, Russian Math. Surveys 42 (1987), 109-180.
    • (1987) Russian Math. Surveys , vol.42 , pp. 109-180
    • Khenkin, G.M.1    Novikov, R.G.2
  • 20
    • 84972498076 scopus 로고
    • Scattering theory for differential operators, I, II
    • S. T. Kuroda, Scattering theory for differential operators, I, II, J. Math. Soc. Japan 25 (1972), 75-104, 222-234.
    • (1972) J. Math. Soc. Japan , vol.25 , pp. 75-104
    • Kuroda, S.T.1
  • 23
    • 84990609931 scopus 로고
    • Determining anisotropic real-analytic conductivity by boundary measurements
    • J. Lee and G. Uhlmann, Determining anisotropic real-analytic conductivity by boundary measurements, Comm. Pure Appl. Math. 42 (1989), 1097-1112.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 1097-1112
    • Lee, J.1    Uhlmann, G.2
  • 25
    • 0000426306 scopus 로고
    • Reconstruction from boundary measurements
    • A. Nachman, Reconstruction from boundary measurements, Ann. of Math. 128 (1988), 531-576.
    • (1988) Ann. of Math. , vol.128 , pp. 531-576
    • Nachman, A.1
  • 26
    • 0030550779 scopus 로고    scopus 로고
    • Global uniqueness for a two dimensional inverse boundary value problem
    • _, Global uniqueness for a two dimensional inverse boundary value problem, Ann. of Math. 143 (1996), 71-96.
    • (1996) Ann. of Math. , vol.143 , pp. 71-96
  • 27
    • 0010533416 scopus 로고
    • The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator
    • R. G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator, J. Fund. Anal. 103 (1992), 409-463.
    • (1992) J. Fund. Anal. , vol.103 , pp. 409-463
    • Novikov, R.G.1
  • 28
    • 38249035778 scopus 로고
    • The Laplace operator on a hyperbolic manifold I. Spectral and scattering theory
    • P. A. Perry, The Laplace operator on a hyperbolic manifold I. Spectral and scattering theory, J. Funct. Anal. 75 (1987), 161-187.
    • (1987) J. Funct. Anal. , vol.75 , pp. 161-187
    • Perry, P.A.1
  • 31
    • 0012094090 scopus 로고
    • On an inverse boundary value problem in two dimensions
    • Z. Sun, On an inverse boundary value problem in two dimensions, Comm. Partial Differential Equations 14 (1989), 1101-1113.
    • (1989) Comm. Partial Differential Equations , vol.14 , pp. 1101-1113
    • Sun, Z.1
  • 32
    • 84974001727 scopus 로고
    • Generic uniqueness for an inverse boundary value problem
    • Z. Sun and G. Uhlmann, Generic uniqueness for an inverse boundary value problem, Duke Math. J. 62 (1991), 131-155.
    • (1991) Duke Math. J. , vol.62 , pp. 131-155
    • Sun, Z.1    Uhlmann, G.2
  • 33
    • 21144461533 scopus 로고
    • Recovery of singularities for formally determined problems
    • _, Recovery of singularities for formally determined problems, Comm. Math. Phys. 153 (1993), 431-445.
    • (1993) Comm. Math. Phys. , vol.153 , pp. 431-445
  • 34
    • 84990586454 scopus 로고
    • An anisotropic inverse boundary problem
    • J. Sylvester, An anisotropic inverse boundary problem, Comm. Pure Appl. Math. 43 (1990), 201-233.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 201-233
    • Sylvester, J.1
  • 35
    • 84990623248 scopus 로고
    • A uniqueness theorem for an inverse boundary value problem in electrical prospection
    • J. Sylvester and G. Uhlmann, A uniqueness theorem for an inverse boundary value problem in electrical prospection, Comm. Pure Appl. Math. 39 (1986), 91-112.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 91-112
    • Sylvester, J.1    Uhlmann, G.2
  • 36
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math. 125 (1987), 153-169.
    • (1987) Ann. of Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.