Isaac Z. Pesenson

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A notion of Paley-Wiener spaces on combinatorial graphs is introduced. 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(More)
Abstract. We prove Poincaré and Plancherel–Polya inequalities for weighted p-spaces on weighted graphs in which the constants are explicitly expressed in terms of some geometric characteristics of a graph. We use a Poincaré-type inequality to obtain some new relations between geometric and spectral properties of the combinatorial Laplace operator. Several(More)
The notion of band limited functions is introduced on a quantum graph. The main results of the paper are a uniqueness theorem and a reconstruction algorithm of such functions from discrete sets of values. It turns out that some of our band limited functions can have compact supports and their frequencies can be localized on the “time” side. It opens an(More)
Analysis on two dimensional surfaces and in particular on the sphere S found many applications in computerized tomography, statistics, signal analysis, seismology, weather prediction, and computer vision. During last years many problems of classical harmonic analysis were developed for functions on manifolds and especially for functions on spheres: splines,(More)
We consider functions on a graph G whose evolution in time - ∞ <; t <; ∞ is governed by a Schrödinger type equation with a combinatorial Laplace operator on the right side. For a given subset S of vertices of G we compute a cut-off frequency ω > 0 such that solutions to a Cauchy problem with initial data in(More)
We consider functions on a weighted combinatorial graph G (finite or countable) whose evolution in time −∞ < t < ∞ is governed by the Schrödinger type equation ∂g(t, v)/∂t = iΔg(t, v), v ∊ V (G), with the combinatorial Laplace operator on the right side. Two Shannon-type sampling(More)