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13 November 2003 Physical laws governing finite tight frames
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Abstract
We give a physical interpretation for finite tight frames along the lines of Columb's Law in Physics. This allows us to use results from classical mechanics to anticipate results in frame theory. As a consequence, we are able to classify those frames for an N-dimensional Hilbert space which are the closest to being tight (in the sense of minimizing potential energy) while having the norms of the frame vectors prescribed in advance. This also yields a fundamental inequality that all finite tight frames must satisfy.
© (2003) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Peter G. Casazza, Matthew C. Fickus, Jelena Kovacevic, Manuel T. Leon, and Janet C. Tremain "Physical laws governing finite tight frames", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.503746
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