title: Canonical forms of unconditionally convergent multipliers.
abstract: 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).
authors.affiliation: Acoustics Research Institute, Wohllebengasse 12-14, Vienna A-1040, Austria.
authors.forename: D T
authors.initials: DT
authors.lastname: Stoeva
authors.forename: P
authors.initials: P
authors.lastname: Balazs
keywords: Bessel sequence; Frame; Multiplier; Riesz basis; Unconditional convergence
references.citation: J Acoust Soc Am. 2011 Feb;129(2):888-97
references.pmid: 21361446