Book chapter
Construction of Multiresolution Analysis Based on Localized Reproducing Kernels
Frames and Other Bases in Abstract and Function Spaces, pp 355-375
12 Jun 2017
Abstract
In this survey paper we show via two examples how multiresolution analysis can be constructed by means of localized reproducing kernels, an alternative to the Fourier technique used in the construction of the affine multiresolution. We consider the Hardy space and the Bergman space of the unit disc. We demonstrate that proper discretizations of two special voice transforms of the Blaschke group lead to analogues of the multiresolution analysis. Our constructions make use of the localization properties of the reproducing kernels restricted to appropriately selected sets of sampling points.
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Details
- Title
- Construction of Multiresolution Analysis Based on Localized Reproducing Kernels
- Creators
- K. Nowak - Drexel UniversityM. Pap - University of Pecs
- Publication Details
- Frames and Other Bases in Abstract and Function Spaces, pp 355-375
- Series
- Applied and Numerical Harmonic Analysis
- Publisher
- Springer International Publishing; Cham
- Resource Type
- Book chapter
- Language
- English
- Academic Unit
- Computer Science (Computing)
- Scopus ID
- 2-s2.0-85047238863
- Other Identifier
- 991019173447204721