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About the book[edit]



Basic definitions and background[edit]

Graphs and manifolds[edit]

Harmonic functions[edit]

On random processes[edit]

Special matrices and determinants[edit]

Electrical networks[edit]

The inverse problems[edit]

Applications to classical 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 new spectral theorems[edit]

The layered case[edit]

Fourier transform[edit]

Stieltjes continued fractions[edit]

Blaschke products[edit]

Pick-Nevanlinna interpolation[edit]

Cauchy matrices[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]


About the author[edit]