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On 2D Inverse Problems edit

by David V. Ingerman edit

About the book
Summary: Summary
Background: Basic definitions and background; Harmonic functions; On random processes; Special matrices and determinants; Electrical networks; The inverse problems
Three classical problems: On the inverse problem of Calderon; "Can One Hear the Shape of a Drum?"; On inhomogeneous string of Krein
Embedded graphs: Medial graphs; Dual graphs and harmonic conjugates; Determining genus of a graph; The new spectral theorem
The layered case: Fourier coordinates; Stieltjes continued fractions; Blaschke products; Pick-Nevanlinna interpolation; Cauchy matrices; Solution of the inverse problem
The square root of minus Laplacian: The case of the unit disc; Zolotarev problem; One more graph example
Discrete and continuous models: Kernel of Dirichlet-to-Neumann map; Riemann mapping theorem; Hilbert transfrom; Schrodinger equation; Variation diminition property; Spectral properties
Notation: Notation
Acknowledgements: Acknowledgements
About the author: About the author
Bibliography: Bibliography