The reconstruction property in Banach spaces generated by matrices
-
Geetika Khattar
and
Lalit Kumar Vashisht
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.
Funding source: R & D Doctoral Research Programme, University of Delhi, Delhi
Award Identifier / Grant number: DRCH/R & D/2013-14/4155
The authors would like to thank the referee for careful reading of the paper and constructive suggestions to improve the paper.
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- On the asymptotics of the generalized Fup-functions
- Approximations of the Mellin transform in the complex domain
- The reconstruction property in Banach spaces generated by matrices
- Isomorphy and dilatation in digraphs
- The C*-algebra of some 6-dimensional nilpotent Lie groups
Articles in the same Issue
- Frontmatter
- On the asymptotics of the generalized Fup-functions
- Approximations of the Mellin transform in the complex domain
- The reconstruction property in Banach spaces generated by matrices
- Isomorphy and dilatation in digraphs
- The C*-algebra of some 6-dimensional nilpotent Lie groups
