Invertibility of multipliers

In the present paper the invertibility of multipliers is investigated in detail. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for invertibility are determined depending on the properties of the a...

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Bibliographic Details
Published in:Applied and computational harmonic analysis 2012-09, Vol.33 (2), p.292-299
Main Authors: Stoeva, D.T., Balazs, P.
Format: Article
Language:English
Subjects:
Bessel sequence
Fourier analysis
Frame
Harmonic analysis
Inverse
Invertibility
Multiplication
Multiplier
Multipliers
Operators
Riesz basis
Symbols
Synthesis
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Summary:In the present paper the invertibility of multipliers is investigated in detail. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples are given, showing that the established bounds are sharp. If a multiplier is invertible, a formula for the inverse operator is determined and n-term error bounds are given. The case when one of the sequences is a Riesz basis is completely characterized.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2011.11.001