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.
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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. 95–111DOI 10.2977/PRIMS/1195164793