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Factor posets of
frames and dual frames in finite dimensions
Kileen Berry, Martin S. Copenhaver, Eric Evert, Yeon Hyang Kim, Troy Klingler, Sivaram K. Narayan and Son T. Nghiem
Vol. 9 (2016), No. 2, 237–248
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Abstract |
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We consider frames in a finite-dimensional Hilbert space, where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of subsets of , the index set of our vectors, ordered by inclusion so that nonempty is in the factor poset if and only if is a tight frame. We first study when a poset is a factor poset of a frame and then relate the two topics by discussing the connections between the factor posets of frames and their duals. Additionally we discuss duals with regard to -minimization. |
Keywords
frames, tight frames, factor poset, $\ell_p$-norm
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Mathematical Subject Classification 2010
Primary: 42C15, 05B20, 15A03
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Milestones
Received: 26 September 2014
Revised: 28 February 2015
Accepted: 27 March 2015
Published: 2 March 2016
Communicated by David Royal Larson
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Authors |
| Kileen Berry | |
| Department of Mathematics University of Tennessee Knoxville, TN 37996 United States |
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| Martin S. Copenhaver | |
| Operations Research Center Massachusetts Institute of Technology Cambridge, MA 02139 United States |
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| Eric Evert | |
| Department of Mathematics University of California, San Diego La Jolla, CA 92093 United States |
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| Yeon Hyang Kim | |
| Department of Mathematics Central Michigan University Mount Pleasant, MI 48859 United States |
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| Troy Klingler | |
| Department of Mathematics Central Michigan University Mount Pleasant, MI 48859 United States |
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| Sivaram K. Narayan | |
| Department of Mathematics Central Michigan University Mount Pleasant, MI 48859 United States |
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| Son T. Nghiem | |
| Berea College Berea, KY 40403 United States |
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