Weighted fusion frame construction via spectral tetris

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces,...

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Bibliographic Details
Published in:Advances in computational mathematics 2014-04, Vol.40 (2), p.335-351
Main Authors: Casazza, Peter G., Peterson, Jesse
Format: Article
Language:English
Subjects:
Computation
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Construction
Frames
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Projection
Spectra
Subspaces
Visualization
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Summary:Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unit-weight fusion frames with these properties is the flexible and elementary procedure known as spectral tetris. Despite the extensive literature on fusion frames, until now there has been no construction of fusion frames with prescribed weights. In this paper we use spectral tetris to construct more general, arbitrarily weighted fusion frames. Moreover, we provide necessary and sufficient conditions for when a desired fusion frame can be constructed via spectral tetris.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-013-9310-7