Publications of the Research Institute for Mathematical Sciences


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Volume 31, Issue 1, 1995, pp. 95–111
DOI: 10.2977/prims/1195164793

General Existence Theorems for Orthonormal Wavelets, an Abstract Approach

Larry Baggett[1], Alan L. Carey[2], William Moran and Peter Ohring[3]

(1) Department of Mathematics, University of Colorado, Campus Box 395, CO 80309-0395, BOULDER, UNITED STATES
(2) Centre for Mathematics and its Applications (MSI), Australian National University, Bldg 27, ACT 0200, CANBERRA, AUSTRALIA
(3) Department of Mathematics, SUNY at Purchase, 735 Anderson Hill Road,, NY, 10577, PURCHASE, UNITED STATES

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.

Keywords:

Baggett L, Carey A, Moran W, Ohring P. General Existence Theorems for Orthonormal Wavelets, an Abstract Approach. Publ. Res. Inst. Math. Sci. 31 (1995), 95-111. doi: 10.2977/prims/1195164793