Canonical forms of unconditionally convergent multipliers

Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in acoustical signal processing. It is known that bounded symbols an...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2013-03, Vol.399 (1), p.252-259
Main Authors: Stoeva, D.T., Balazs, P.
Format: Article
Language:English
Subjects:
Bessel sequence
Frame
Multiplier
Riesz basis
Unconditional convergence
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Summary:Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in acoustical signal processing. It is known that bounded symbols and Bessel sequences guarantee unconditional convergence. In this paper we investigate necessary and equivalent conditions for the unconditional convergence of multipliers. In particular, we show that, under mild conditions, unconditionally convergent multipliers can be transformed by shifting weights between symbol and sequence, into multipliers with symbol (1) and Bessel sequences (called multipliers in canonical form).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.10.007