General Existence Theorems for Orthonormal Wavelets, an Abstract Approach

Larry Baggett; Alan L. Carey; William Moran; Peter Ohring

doi:10.2977/prims/1195164793

JournalsprimsVol. 31, No. 1pp. 95–111

General Existence Theorems for Orthonormal Wavelets, an Abstract Approach

Larry Baggett
University of Colorado, Boulder, USA
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- zbMATH Open
Alan L. Carey
The Australian National University, Canberra, Australia
- MathSciNet
- zbMATH Open
William Moran
The University of Adelaide, Australia
- MathSciNet
- zbMATH Open
Peter Ohring
SUNY at Purchase, USA
- MathSciNet
- zbMATH Open

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Abstract

Methods from noncommutative harmonic analysis are used to develop an abstract theory of orthonormal wavelets. The relationship between the existence of an orthonormal wavelet and the existence of a multi-resolution is clarified, and four theorems guaranteeing the existence of wavelets are proved. As a special case of the fourth theorem, a generalization of known results on the existence of smooth wavelets having compact support is obtained.

Cite this article

Larry Baggett, Alan L. Carey, William Moran, Peter Ohring, General Existence Theorems for Orthonormal Wavelets, an Abstract Approach. Publ. Res. Inst. Math. Sci. 31 (1995), no. 1, pp. 95–111

DOI 10.2977/PRIMS/1195164793