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Inverse boundary value problems for discrete Schrödinger operators on the multi-dimensional square lattice
| 1. | Graduate school of pure and applied sciences, University of Tsukuba, Tennnoudai 1-1-1, Tsukuba, Ibaraki, 305-0821, Japan |
References:
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K. Ando, Inverse scattering theory for discrete Schrödinger operators on the hexagonal lattice,, preprint., ().
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L. Borcea, V. Druskin and A. Mamonov, Circular resistor networks for electrical impedance tomography with partial boundary measurements, Inverse Problems, 26 (2010), 30 pp.
doi: 10.1088/0266-5611/26/4/045010. |
| [3] |
L. Borcea, V. Druskin, A. Mamonov and F. Guevara Vasquez, Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements, Inverse Problems, 26 (2010), 36 pp.
doi: 10.1088/0266-5611/26/10/105009. |
| [4] |
F. R. Chung, "Spectral Graph Theory," CBMS Regional Conference Series in Mathematics, 92, AMS, Providence, RI, 1997. |
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E. Curtis and J. Morrow, The Dirichlet to Neumann map for a resistor network, SIAM J. Appl. Math., 51 (1991), 1011-1029.
doi: 10.1137/0151051. |
| [6] |
E. Curtis, E. Mooers and J. Morrow, Finding the conductors in circular networks from boundary measurements, RAIRO Modél. Math. Anal. Numér., 28 (1994), 781-814. |
| [7] |
R. Diestel, "Graph Theory," 2nd edition, Graduate Texts in Mathematics, 173, Springer-Verlag, New York, 2000. |
| [8] |
H. Isozaki and E. Korotyaev, Inverse problems, trace formulae for discrete Schrödinger operators,, submitted., ().
|
| [9] |
H. Isozaki, Some remarks on the multi-dimensional Borg-Levinson theorem, J. Math. Kyoto Univ., 31 (1991), 743-753. |
| [10] |
R. G. Novikov and G. M. Khenkin, The $\overline\partial$-equation in the multidimensional inverse scattering problem, (Russian) Uspekhi Mat. Nauk, 42 (1987), 93-152, 255. |
| [11] |
A. I. Nachman, Reconstruction from boundary measurements, Ann. Math. (2), 128 (1988), 531-576.
doi: 10.2307/1971435. |
| [12] |
A. I. Nachman, J. Sylvester and G. Uhlmann, An $n$-dimensional Borg-Levinson theorem, Commun. Math. Phys., 115 (1988), 595-605.
doi: 10.1007/BF01224129. |
| [13] |
R. Oberlin, Discrete inverse problems for Schrödinger and resistor networks, Research archive of Research Experiences for Undergraduates program at Univ. of Washington, 2000. Available from: http://www.math.washington.edu/~reu//papers/2000/oberlin/oberlin_schrodinger.pdf. |
| [14] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. Math. (2), 125 (1987), 153-169.
doi: 10.2307/1971291. |
show all references
References:
| [1] |
K. Ando, Inverse scattering theory for discrete Schrödinger operators on the hexagonal lattice,, preprint., ().
|
| [2] |
L. Borcea, V. Druskin and A. Mamonov, Circular resistor networks for electrical impedance tomography with partial boundary measurements, Inverse Problems, 26 (2010), 30 pp.
doi: 10.1088/0266-5611/26/4/045010. |
| [3] |
L. Borcea, V. Druskin, A. Mamonov and F. Guevara Vasquez, Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements, Inverse Problems, 26 (2010), 36 pp.
doi: 10.1088/0266-5611/26/10/105009. |
| [4] |
F. R. Chung, "Spectral Graph Theory," CBMS Regional Conference Series in Mathematics, 92, AMS, Providence, RI, 1997. |
| [5] |
E. Curtis and J. Morrow, The Dirichlet to Neumann map for a resistor network, SIAM J. Appl. Math., 51 (1991), 1011-1029.
doi: 10.1137/0151051. |
| [6] |
E. Curtis, E. Mooers and J. Morrow, Finding the conductors in circular networks from boundary measurements, RAIRO Modél. Math. Anal. Numér., 28 (1994), 781-814. |
| [7] |
R. Diestel, "Graph Theory," 2nd edition, Graduate Texts in Mathematics, 173, Springer-Verlag, New York, 2000. |
| [8] |
H. Isozaki and E. Korotyaev, Inverse problems, trace formulae for discrete Schrödinger operators,, submitted., ().
|
| [9] |
H. Isozaki, Some remarks on the multi-dimensional Borg-Levinson theorem, J. Math. Kyoto Univ., 31 (1991), 743-753. |
| [10] |
R. G. Novikov and G. M. Khenkin, The $\overline\partial$-equation in the multidimensional inverse scattering problem, (Russian) Uspekhi Mat. Nauk, 42 (1987), 93-152, 255. |
| [11] |
A. I. Nachman, Reconstruction from boundary measurements, Ann. Math. (2), 128 (1988), 531-576.
doi: 10.2307/1971435. |
| [12] |
A. I. Nachman, J. Sylvester and G. Uhlmann, An $n$-dimensional Borg-Levinson theorem, Commun. Math. Phys., 115 (1988), 595-605.
doi: 10.1007/BF01224129. |
| [13] |
R. Oberlin, Discrete inverse problems for Schrödinger and resistor networks, Research archive of Research Experiences for Undergraduates program at Univ. of Washington, 2000. Available from: http://www.math.washington.edu/~reu//papers/2000/oberlin/oberlin_schrodinger.pdf. |
| [14] |
J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. Math. (2), 125 (1987), 153-169.
doi: 10.2307/1971291. |
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