Last modified on 21 July 2013, at 09:22

On 2D Inverse Problems/Bibliography

  1. [AP] Astala, K. and P¨aiv¨arinta, L. "Calder´on’s inverse conductivity problem in the plane", http://annals.math.princeton.edu/wp-content/uploads/annals-v163-n1-p05.pdf
  2. [BIMS] Biesel, O. D., Ingerman D. V., Morrow J. A. and Shore W. T. "Layered Networks, the Discrete Laplacian, and a Continued Fraction Identity", http://www.math.washington.edu/~reu/papers/2008/william/layered.pdf
  3. [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)
  4. [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
  5. [Ca] Cannon, J. W. "The combinatorial Riemann mapping theorem", http://www.springerlink.com/content/9w0608p039151254/
  6. [CM] Curtis, E. B. and Morrow, J. A. "Inverse Problems for Electrical Networks", http://books.google.com/books/about/Inverse_Problems_for_Electrical_Networks.html?id=gLnohh95zFIC
  7. [CIM] Curtis, E. B., Ingerman, D. V. and Morrow, J. A. "Circular Planar Graphs and Resistor Networks", http://www.math.washington.edu/~morrow/papers/cim.pdf
  8. [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.
  9. [DeV1] De Verdière, Yves Colin, "Réseaux électriques planaires", Prépublications de l'Institut Fourier 225 (1992), 1-20
  10. [DeV2] De Verdière, Yves Colin, "Reseaux electrique planaires I", http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.133
  11. [DS] Doyle, P. G. and Snell, L. J. "Random walks and electric networks", http://www.cse.buffalo.edu/~hungngo/classes/2005/Expanders/papers/general/randomWalk.pdf
  12. [DIK] Druskin, V., Ingerman D. V. and Knizhnerman, L. "Optimal finite difference grids and rational approximations of the square root I. Elliptic problems", http://onlinelibrary.wiley.com/doi/10.1002/1097-0312(200008)53:8%3C1039::AID-CPA4%3E3.0.CO;2-I/abstract
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  16. [GK] Gantmacher, F. R. and Krein, M. G. "Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems", Revised Edition, http://www.ams.org/bookstore?fn=20&arg1=diffequ&ikey=CHEL-345-H
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  19. [I1] Ingerman, D. V. "The Square of the Dirichlet-to-Neumann map equals minus Laplacian", http://arxiv.org/ftp/arxiv/papers/0806/0806.0653.pdf
  20. [I2] Ingerman, D. V. "Discrete and continuous inverse boundary problems on a disc", PhD thesis, 1997, http://www.math.washington.edu/~morrow/papers/ingerman.pdf
  21. [JT] Jones, W. B. and Thron, W. J. "Continued Fractions: Analytic Theory and Applications", http://books.google.com/books?id=Cy2NPwAACAAJ&dq=Jones,+Continued+fractions&source=bl&ots=_qZqYUwb9g&sig=829uHGccJUlhQCum7OD4rsWe0dg&hl=en&sa=X&ei=1alfUO32MoqyiQLWkYHIBA&ved=0CDcQ6AEwAQ
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  26. [LST] LASSAS, M., SALO, M., and TZOU, L. "INVERSE PROBLEMS AND INVISIBILITY CLOAKING FOR FEM MODELS AND RESISTOR NETWORKS", http://arxiv.org/pdf/1307.1539.pdf
  27. [M] Marshall, D. E. "An elementary proof of the Pick-Nevanlinna interpolation theorem", http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.mmj/1029001307&page=record
  28. [N] Nachman, A. I. "Global uniqueness for a two-dimensional inverse boundary value problem", http://www.jstor.org/discover/10.2307/2118653?uid=3739960&uid=2&uid=4&uid=3739256&sid=21101022816693
  29. [PU] Pestov, L. and Uhlmann, G. "Two dimensional compact simple Riemannian manifolds are boundary distance rigid", http://annals.math.princeton.edu/2005/161-2/p12
  30. [PP] Petrushev, P. P. and Popov, A. V. "Rational approximation of real functions", 1987, http://books.google.com/books/about/Rational_Approximation_of_Real_Functions.html?id=0up9c_uo2xQC
  31. [P] Pinkus, A. "Totally positive matrices", http://www.amazon.com/Totally-Positive-Matrices-Cambridge-Mathematics/dp/0521194083
  32. [S] Seidman, T. I. "An inverse eigenvalue problem with rotational symmetry", http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.76.3752&rep=rep1&type=pdf
  33. [SU] Sylvester, J. and Uhlmann, G. "A global uniqueness theorem for an inverse boundary value problem", Ann. of Math., 125 (1987), 153–169.
  34. [Uh] Uhlmann, G. "Electrical impedance tomography and Calder´on’s problem", http://www.math.washington.edu/~gunther/publications/Papers/calderoniprevised.pdf
  35. [Us] Ustinov A. V. "A Discrete Analog of the Poisson Summation Formula", http://link.springer.com/article/10.1023%2FA%3A1022178118555?LI=true

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