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 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) Mathematical Sciences Institute, The Australian National University, John Dedman Building 27, Union Lane, ACT 2601, 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.


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