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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Frames and the Feichtinger conjecture
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by Peter G. Casazza, Ole Christensen, Alexander M. Lindner and Roman Vershynin PDF
Proc. Amer. Math. Soc. 133 (2005), 1025-1033 Request permission

Abstract:

We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linearly independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences.
References
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Additional Information
  • Peter G. Casazza
  • Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
  • MR Author ID: 45945
  • Email: pete@math.missouri.edu
  • Ole Christensen
  • Affiliation: Department of Mathematics, Technical University of Denmark, Building 303, 2800 Lyngby, Denmark
  • MR Author ID: 339614
  • Email: Ole.Christensen@mat.dtu.dk
  • Alexander M. Lindner
  • Affiliation: Center of mathematical Sciences, Munich University of Technology, Boltzmannstr. 3, D-85747 Garching, Germany
  • MR Author ID: 648186
  • Email: lindner@mathematik.tu-muenchen.de
  • Roman Vershynin
  • Affiliation: Department of Mathematics, University of California at Davis, One Shields Avenue, Davis, California 95016
  • MR Author ID: 636015
  • Email: vershynin@math.ucdavis.edu
  • Received by editor(s): February 18, 2003
  • Received by editor(s) in revised form: July 3, 2003
  • Published electronically: November 19, 2004
  • Additional Notes: The first author was supported by NSF DMS 0102686
    The last author thanks PIMS for support
  • Communicated by: David R. Larson
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1025-1033
  • MSC (2000): Primary 46C05, 46L05; Secondary 42C40
  • DOI: https://doi.org/10.1090/S0002-9939-04-07594-X
  • MathSciNet review: 2117203