On 2D Inverse Problems/Bibliography
[AP] Astala, K. and P¨aiv¨arinta, L.
"Calder´on’s inverse conductivity problem in the plane" [BIMS] Biesel, O.D., Ingerman D.V., Morrow J.A. and Shore W.T.
"Layered Networks, the Discrete Laplacian, and a Continued Fraction Identity" [BDK] Borcea, L., Druskin, V. and Knizhnerman, L. "On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids", Communications on Pure and Applied Mathematics, Vol. 000, 0001–0048 (2000)
[BDMV] Borcea, L., Druskin, V., Mamonov, A.V. and Vasquez, G.F. "Resistor network approaches to electrical impedance tomography",
http://arxiv.org/abs/1107.0343 [CM] Curtis, E.B. and Morrow, J.A.
"Inverse Problems for Electrical Networks" [CIM] Curtis, E.B., Ingerman, D.V. and Morrow, J.A.
"Circular Planar Graphs and Resistor Networks" [CMM] Curtis, E.B., Mooers, E. and Morrow J.A. "Finding the conductors in circular networks from boundary measurements", RAIRO Model Math. Anal. Numer. 28 (1994), pp. 781-814.
[DeV1] De Verdière, Yves Colin, "Réseaux électriques planaires", Prépublications de l'Institut Fourier 225 (1992), 1-20
[DeV2] De Verdière, Yves Colin,
"Reseaux electrique planaires I" [DIK] Druskin, V., Ingerman D.V. and Knizhnerman, L.
"Optimal finite difference grids and rational approximations of the square root I. Elliptic problems" [ES] Edelman, A. and Strang, G.
"Pascal matrices" [F] Fomin, S. "Loop-erased walks and total positivity",
http://arxiv.org/pdf/math.CO/0004083.pdf [GK] Gantmacher, F. R. and Krein, M. G.
"Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems", Revised Edition [IM] Ingerman, D.V. and Morrow, J.A.
"On a Characterization of the Kernel of the Dirichlet-to-Neumann Map for a Planar Region" [I2] Ingerman, D.V.
"Discrete and continuous inverse boundary problems on a disc", PhD thesis, 1997 [K] Kac, M. "Can one hear the shape of a drum?", American Mathematical Monthly 73 (4, part 2): 1–23, (1966), doi:10.2307/2313748
[KK] Kac, I.S. and Krein, K.G. "On the spectral function of the string", AMS Translations, 1974, S. 2, 103, 19-102
[M] Marshall, D.E.
"An elementary proof of the Pick-Nevanlinna interpolation theorem" [N] Nachman, A.I.
"Global uniqueness for a two-dimensional inverse boundary value problem" [PU] Pestov, L. and Uhlmann, G.
"Two dimensional compact simple Riemannian manifolds are boundary distance rigid" [SU] Sylvester, J. and Uhlmann, G. "A global uniqueness theorem for an inverse boundary value problem", Ann. of Math., 125 (1987), 153–169