General Existence Theorems for Orthonormal Wavelets, an Abstract Approach
Larry Baggett, Alan L. Carey, William Moran, Peter Ohring · Publications of the Research Institute for Mathematical Sciences · 1995
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.