Canonical forms of unconditionally convergent multipliers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:399

Article

Stoeva, D. T.¹  Balazs, P.¹ 

[1] Acoust Res Inst, A-1040 Vienna, Austria

关键词: Multiplier;    Unconditional convergence;    Frame;    Riesz basis;    Bessel sequence;   

DOI  :  10.1016/j.jmaa.2012.10.007

来源: Elsevier

【 摘 要 】

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). (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free