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Weighted fusion frame construction via spectral tetris

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211-4100, USA

    Peter G. Casazza

  2. Department of Mathematics & Statistics, Air Force Institute of Technology, Wright-Patterson AFB, OH, 45433-7765, USA

    Jesse Peterson

Authors
  1. Peter G. Casazza
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  2. Jesse Peterson
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Correspondence to Jesse Peterson.

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Communicated by: Qiyu Sun

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Casazza, P.G., Peterson, J. Weighted fusion frame construction via spectral tetris. Adv Comput Math 40, 335–351 (2014). https://doi.org/10.1007/s10444-013-9310-7

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  • DOI: https://doi.org/10.1007/s10444-013-9310-7

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