Sampling in paley-wiener spaces on combinatorial graphs

Details Sampling in paley-wiener spaces on combinatorial graphs Sampling in paley-wiener spaces on combinatorial graphs

2011-11-25

arxiv.org/abs/1111.5896v1

Mathematics

Spectral Theory

Transactions of the American Mathematical Society Volume 360, Number 10, October 2008, Pages 5603--5627

Scientific paper

A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such uniqueness sets are described in terms of Poincare-Wirtingertype inequalities. A reconstruction algorithm of Paley-Wiener functions from uniqueness sets which uses the idea of frames in Hilbert spaces is developed. Special consideration is given to n-dimensional lattice, homogeneous trees, and eigenvalue and eigenfunction problems on finite graphs.

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