On 2D Inverse Problems

From Wikibooks, open books for an open world
Jump to: navigation, search
On 2D Inverse Problems


Wikibooks version


For Nicole DeLaittre
Book cover.jpg


About the book[edit]

Summary[edit]

Basic definitions[edit]

Graphs and manifolds[edit]

Harmonic functions[edit]

On random processes[edit]

Special matrices and determinants[edit]

Electrical networks[edit]

The inverse problems[edit]

Classical inverse problems[edit]

On the inverse problem of Calderon[edit]

"Can One Hear the Shape of a Drum?"[edit]

On inhomogeneous string of Krein[edit]

Embedded graphs[edit]

Medial graphs[edit]

Y-Δ and star-mesh transforms[edit]

Two spectral theorems[edit]

The layered case[edit]

Fourier transform[edit]

Stieltjes continued fractions[edit]

Solution of the inverse problem[edit]

The square root of the minus Laplacian[edit]

The case of the unit disc[edit]

An infinite example[edit]

Zolotarev problem[edit]

Discrete and continuous models[edit]

Kernel of Dirichlet-to-Neumann map[edit]

Riemann mapping theorem[edit]

Hilbert transform[edit]

Schrodinger equation[edit]

Variation diminishing property[edit]

Spectral properties[edit]

Notation[edit]

Bibliography[edit]

Acknowledgements[edit]

The author would like to thank Wiki, StackExchange and Sage projects for the help in writing the book @ all stages of the process.

About the author[edit]