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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sampling in Paley-Wiener spaces on combinatorial graphs


Author: Isaac Pesenson
Journal: Trans. Amer. Math. Soc. 360 (2008), 5603-5627
MSC (2000): Primary 42C99, 05C99, 94A20; Secondary 94A12
Published electronically: May 21, 2008
Erratum: Trans. Amer. Math. Soc. 361 (2009), 3951-3951.
MathSciNet review: 2415088
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Abstract: 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-Wirtinger-type 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 the $ n$-dimensional lattice, homogeneous trees, and eigenvalue and eigenfunction problems on finite graphs.


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Additional Information

Isaac Pesenson
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: pesenson@temple.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04511-X
PII: S 0002-9947(08)04511-X
Keywords: Combinatorial graph, combinatorial Laplace operator, discrete Paley-Wiener spaces, Shannon sampling, discrete Plancherel-Polya and Poincare inequalities.
Received by editor(s): August 18, 2006
Received by editor(s) in revised form: March 12, 2007
Published electronically: May 21, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.