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The reconstruction property in Banach spaces generated by matrices

The reconstruction property in Banach spaces generated by matrices Abstract. The reconstruction property for Banach spaces was introduced by Casazza and Christensen. In this paper we give a type of the reconstruction property in Banach spaces which is generated by the Toeplitz matrices and we call it the Toeplitz reconstruction property. It is proved that the standard reconstruction property in a Banach space can generate the Toeplitz reconstruction property from a given Toeplitz matrix but not conversely. Sufficient conditions on infinite matrices to have the reconstruction property for a discrete signal space are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

The reconstruction property in Banach spaces generated by matrices

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam-2014-0022
Publisher site
See Article on Publisher Site

Abstract

Abstract. The reconstruction property for Banach spaces was introduced by Casazza and Christensen. In this paper we give a type of the reconstruction property in Banach spaces which is generated by the Toeplitz matrices and we call it the Toeplitz reconstruction property. It is proved that the standard reconstruction property in a Banach space can generate the Toeplitz reconstruction property from a given Toeplitz matrix but not conversely. Sufficient conditions on infinite matrices to have the reconstruction property for a discrete signal space are given.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Aug 1, 2014

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