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The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates

Published online by Cambridge University Press:  20 November 2018

Marcin Bownik  and
Darrin Speegle
Marcin Bownik
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A. e-mail: mbownik@uoregon.edu
Darrin Speegle
Affiliation:
Department of Mathematics and Computer Science, Saint Louis University, 221 N. Grand Blvd., St. Louis, MO 63103, U.S.A. e-mail: speegled@slu.edu
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Abstract

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The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.

Keywords

42B2542B3542C40frameRiesz basic sequencewaveletGabor systemframe of translatespaving conjecture
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 6 , 01 December 2006 , pp. 1121 - 1143
Copyright
Copyright © Canadian Mathematical Society 2006

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