## 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.

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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