Plancherel inversion as unified approach to wavelet transforms and Wigner functions. (English) Zbl 1049.81043
The authors demonstrate how the Plancherel transform for Type-I groups provide a unified point of view for both the continuous wavelet transform and a class of Wigner functions. In particular they show how, under suitable restrictions, the wavelet transform can be seen as inverse Plancherel transform, and Wigner functions as Fourier transform of inverse Plancherel transform. This standpoint allows to recover in a unified perspective known results on both Wigner functions and wavelet transforms. The authors also provide examples for specific groups.
Reviewer: Bassano Vacchini (Milano)
MSC:
81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |