# On 2D Inverse Problems/Bibliography

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- [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