On 2D Inverse Problems/Basic definitions and background

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