Basic definition and properties of Bessel multipliers
By Peter Balazs. 2005
149 citations recorded by the source corpus.
This 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.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing
View Paper: https://www.semanticscholar.org/paper/09b5494a4d4710c90a6160affc6c8c679e29da27
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Signal Processing
Citations in the corpus
- Invertibility of multipliers (2009, background): “In [4] the concept of Bessel multipliers, i.”