Spectral Tetris Fusion Frame Constructions

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Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of fusion frames. We first show how the assumption on the spectrum of the frame operator can be dropped and extend the spectral tetris algorithm to construct unit norm frames with any given spectrum of the frame operator. We then provide a suffcient condition for using this generalization of spectral tetris to construct fusion frames with prescribed spectrum for the fusion frame operator and with prescribed dimensions for the subspaces. This condition is shown to be necessary in the tight case of redundancy greater than two.


The "Link to Full Text" button on this page loads the open access e-print at arXiv:1108.4061 [math.NA].
Date of arXiv submission: 19 Aug 2011 (v1), revised 9 Jan 2012 (v2)

Reviewed at MR2984371

The publisher's digital version of record for the article is hosted at SpringerLink as a subscription-access article. The citation to the final article is noted below.



Source Publication

Journal of Fourier Analysis and Applications