On the invertibility of “rectangular” bi-infinite matrices and applications in time–frequency analysis

Finite dimensional matrices with more columns than rows have no left inverses while those with more rows than columns have no right inverses. We give generalizations of these simple facts to bi–infinite matrices. Our results are then used to obtain density results for p-frames of time–frequency mole...

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Bibliographic Details
Published in:Linear algebra and its applications 2008-07, Vol.429 (1), p.331-345
Main Author: Pfander, Götz E.
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Gabor frames
Kohn–Nirenberg symbol
Linear and multilinear algebra, matrix theory
Mathematics
Operator identification
Sciences and techniques of general use
Slanted/skew diagonal matrices
Spreading function
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Summary:Finite dimensional matrices with more columns than rows have no left inverses while those with more rows than columns have no right inverses. We give generalizations of these simple facts to bi–infinite matrices. Our results are then used to obtain density results for p-frames of time–frequency molecules in modulation spaces and identifiability results for operators with bandlimited Kohn–Nirenberg symbols.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2008.02.025