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On 2D Inverse Problems
[edit | edit source]by David V. Ingerman
[edit | edit source]- About the book
- Summary
- Summary
- Background
- Graphs and manifolds
- 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
- Y-Δ and star-mesh transforms
- Medial graphs
- Dual graphs and harmonic conjugates
- Determining genus of a graph
- Hamilton paths in graphs
- 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
- One more graph example
- Zolotarev problem
- 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
- Bibliography
- Bibliography
- About the author