Variational Splines and Paley–Wiener Spaces on Combinatorial Graphs |
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Authors: | Isaac Pesenson |
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Institution: | (1) Department of Mathematics, Temple University, Philadelphia, PA 19122, USA |
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Abstract: | Notions of interpolating variational splines and Paley–Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator on G. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational
splines, the paper presents a reconstruction algorithm of Paley–Wiener functions on graphs from their uniqueness sets.
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Keywords: | Combinatorial graph Combinatorial Laplace operator Variational splines Paley– Wiener spaces Interpolation Approximation Reconstruction |
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