Frames and the Feichtinger conjecture

We show that the conjectured generalization of the Bourgain-Tzafriri {\it restricted-invertibility theorem} is equivalent to the conjecture of\linebreak 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 lea...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-04, Vol.133 (4), p.1025-1033
Main Authors: CASAZZA, Peter G, CHRISTENSEN, Ole, LINDNER, Alexander M, VERSHYNIN, Roman
Format: Article
Language:English
Subjects:
Eigenvalues
Exact sciences and technology
Fourier analysis
Functional analysis
Hilbert spaces
Integers
Linear transformations
Mathematical analysis
Mathematical constants
Mathematical sequences
Mathematical theorems
Mathematics
Natural numbers
Scalars
Sciences and techniques of general use
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Summary:We show that the conjectured generalization of the Bourgain-Tzafriri {\it restricted-invertibility theorem} is equivalent to the conjecture of\linebreak 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 {\it paving conjecture}. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-04-07594-X