Journal of Fourier Analysis and Applications

, Volume 3, Issue 4, pp 451–456

Wavelet sets in ℝn

  • Xingde Dai
  • David R. Larson
  • Darrin M. Speegle
Article

DOI: 10.1007/BF02649106

Cite this article as:
Dai, X., Larson, D.R. & Speegle, D.M. The Journal of Fourier Analysis and Applications (1997) 3: 451. doi:10.1007/BF02649106

Abstract

A congruency theorem is proven for an ordered pair of groups of homeomorphisms of a metric space satisfying an abstract dilation-translation relationship. A corollary is the existence of wavelet sets, and hence of single-function wavelets, for arbitrary expansive matrix dilations on L2(n). Moreover, for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the Borel structure ofn.

Copyright information

© CRC Press LLC 1997

Authors and Affiliations

  • Xingde Dai
    • 1
  • David R. Larson
    • 2
  • Darrin M. Speegle
    • 2
  1. 1.Department of MathematicsUniv. of North CarolinaCharlotte
  2. 2.Department of MathematicsTexas A&M UniversityCollege Station