On 2D Inverse Problems/Basic definitions and background

The main subjects of study of this book are the local and global characteristices of graphs embedded in surfaces (2D manifolds) and the connections b/w their discrete and continuous properties. This chapter gives the definitions and the overview of the main mathematical objects that are involved in the inverse problems discussed in the book. These include the domains of definitions of the functions and operators, the boundary and spectral data and interpolation/extrapolation and restriction techniques.

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Graphs and surfaces

Harmonic functions

On random processes

Special matrices and determinants

Electrical networks

The inverse problems