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Matrix representation of operators using frames.(Technical report)
- Article from:
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Sampling Theory in Signal and Image Processing
- Article date:
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January 1, 2008
- Author:
- Balazs, Peter
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Copyright informationCOPYRIGHT 2008 Sampling Publishing. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract
This paper addresses how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames, and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore, it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on [l.sup.2] and operators on H. We will show some structural results and give some examples. Furthermore, in the case of Riesz bases we prove that those functions are isomorphisms. Finally we ...
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