Wavelets have recently been enjoying a period of popularity and rapid growth, and the influence of wavelet methods now extends well beyond mathematics into a number of practical fields, including statistics. The theory of hypergroups can be traced back to the turn of the century, and following its formalization in the early 1970s, the area has now reached maturity.
Hypergroups provide a very general and flexible context in which many of the classical techniques of harmonic analysis can be fruitfully employed. It is, therefore, natural to seek to exploit the newer techniques of wavelet analysis in this area. This text addresses itself to this challenge in some depth, providing a thorough and authoritative account of wavelet methods applied to hypergroups.
Table of Contents
1. Hypergroups 2. Wavelets and the Windowed Spherical Fourier Transform on Gelfand Pairs 3. Generalized Wavelets and Generalized Continuous Wavelet Transforms on Hypergroups 4. Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform Associated with the Spherical Mean Operator 5.
Generalized Radon Transforms on Generalized Hypergroups 6. Inversion of Generalized Radon Transforms Using Generalized Wavelets 7. Product Formulas and Generalized Hypergroups 8. Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform on Chébli-Trimèche 9. Hypergroups
Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform Associated with Laguerre Functions 10. Generalized Wavelets and Generalized Continuous Wavelet Transforms on Semisimple Lie Groups and on Cartan Motion Groups