Sampling in Paley-Wiener spaces on combinatorial graphs
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Erratum: Trans. Amer. Math. Soc. 361 (2009), 3951-3951.
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.References
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Additional Information
- Isaac Pesenson
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- MR Author ID: 196903
- Email: pesenson@temple.edu
- Received by editor(s): August 18, 2006
- Received by editor(s) in revised form: March 12, 2007
- Published electronically: May 21, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 5603-5627
- MSC (2000): Primary 42C99, 05C99, 94A20; Secondary 94A12
- DOI: https://doi.org/10.1090/S0002-9947-08-04511-X
- MathSciNet review: 2415088