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- Title
Weighted fusion frame construction via spectral tetris.
- Authors
Casazza, Peter; Peterson, Jesse
- Abstract
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.
- Subjects
FUSION (Phase transformation); HILBERT space; ORTHOGRAPHIC projection; SUBSPACES (Mathematics); ALGORITHM research; DISCRETE Fourier transforms
- Publication
Advances in Computational Mathematics, 2014, Vol 40, Issue 2, p335
- ISSN
1019-7168
- Publication type
Academic Journal
- DOI
10.1007/s10444-013-9310-7