JournalsprimsVol. 31 , No. 1DOI 10.2977/prims/1195164793

General Existence Theorems for Orthonormal Wavelets, an Abstract Approach

  • Larry Baggett

    University of Colorado, Boulder, USA
  • Alan L. Carey

    The Australian National University, Canberra, Australia
  • William Moran

    The University of Adelaide, Australia
  • Peter Ohring

    SUNY at Purchase, USA
General Existence Theorems for Orthonormal Wavelets, an Abstract Approach cover

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.