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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Frames and the Feichtinger conjecture


Authors: Peter G. Casazza, Ole Christensen, Alexander M. Lindner and Roman Vershynin
Journal: Proc. Amer. Math. Soc. 133 (2005), 1025-1033
MSC (2000): Primary 46C05, 46L05; Secondary 42C40
Published electronically: November 19, 2004
MathSciNet review: 2117203
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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.


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Additional Information

Peter G. Casazza
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email: pete@math.missouri.edu

Ole Christensen
Affiliation: Department of Mathematics, Technical University of Denmark, Building 303, 2800 Lyngby, Denmark
Email: Ole.Christensen@mat.dtu.dk

Alexander M. Lindner
Affiliation: Center of mathematical Sciences, Munich University of Technology, Boltzmannstr. 3, D-85747 Garching, Germany
Email: lindner@mathematik.tu-muenchen.de

Roman Vershynin
Affiliation: Department of Mathematics, University of California at Davis, One Shields Avenue, Davis, California 95016
Email: vershynin@math.ucdavis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07594-X
PII: S 0002-9939(04)07594-X
Keywords: Kadison-Singer problem, paving conjecture, Feichtinger conjecture, frames
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
Article copyright: © Copyright 2004 American Mathematical Society