This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a reasonably self-contained exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.

Includes supplementary material: sn.pub/extras

Inhalt
Introduction.- Wavelet Transforms and Group Representations.- The Plancherel Transform for Locally Compact Groups.- Plancherel Inversion and Wavelet Transforms.- Admissible Vectors for Group Extension.- Sampling Theorems for the Heisenberg Group.- References.- Index.