Basic definition and properties of Bessel multipliers

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dc.creatorBalazs, Peter
dc.date2005-10-05
dc.date2006-11-20
dc.date.accessioned2026-07-07T06:47:10Z
dc.date.available2026-07-07T06:47:10Z
dc.descriptionThis paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the Analysis and synthesis operators. The proposed concept unifies the approach used for Gabor multipliers for arbitrary analysis/synthesis systems, which form Bessel sequences, like wavelet or irregular Gabor frames. The basic properties of this class of operators are investigated. In particular the implications of summability properties of the symbol for the membership of the corresponding operators in certain operator classes are specified. As a special case the multipliers for Riesz bases are examined and it is shown that multipliers in this case can be easily composed and inverted. Finally the continuous dependence of a Bessel multiplier on the parameters (i.e. the involved sequences and the symbol in use) is verified, using a special measure of similarity of sequences.
dc.description15 pages; Paper was cut from 27 to 15 pages and got a new title
dc.identifierhttps://arxiv.org/abs/math/0510091
dc.identifierhttp://arxiv.org/abs/math/0510091
dc.identifierJournal of Mathematical Analysis and Applications 325 (2007) pp. 571-585
dc.identifierdoi:10.1016/j.jmaa.2006.02.012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103568
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject41A58; 47L15; 46C05; 47B10
dc.titleBasic definition and properties of Bessel multipliers
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