Journal article
Geometric Structures of Frequency Domains of Band-Limited Scaling Functions and Wavelets
Acta Applicandae Mathematicae, Vol.131(1), pp.141-154
06/2014
DOI: 10.1007/s10440-013-9851-2
Abstract
The support of the Fourier transform of a wavelet is said to be its frequency domain. In the research of geometric structures of frequency domains of band-limited wavelets, it is well known that the frequency domain of any band-limited wavelet has a hole, in which the origin lies. In Zhang (J. Approx. Theory 148:128–147, 2007), we further study measures, densities, and diameters of frequency domains of band-limited wavelets. The measure of the frequency domain of any wavelet is ≥2π. If the measure is 2π, then such a wavelet is said to be a minimally supported frequency (MSF) wavelet. In this paper, we will show that the frequency domain of any band-limited MRA wavelet contains that of some MSF wavelet. Meanwhile, we will discuss the geometric structure of the frequency domain of the corresponding scaling function.
Details
- Title: Subtitle
- Geometric Structures of Frequency Domains of Band-Limited Scaling Functions and Wavelets
- Creators
- Zhihua Zhang - Beijing Normal UniversityPalle Jorgensen - Department of Mathematics University of Iowa Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Acta Applicandae Mathematicae, Vol.131(1), pp.141-154
- Publisher
- Springer Netherlands; Dordrecht
- DOI
- 10.1007/s10440-013-9851-2
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- Language
- English
- Date published
- 06/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985976402771
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