Analysis und Zahlentheorie
Prof. Dr. A. Krieg
Springer Lecture Notes in Mathematics, Nr. 1863
2005, X, 193 p., Softcover
ISBN: 3-540-24259-7
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.
Text Samples (in pdf format): Preface Table of Contents Introduction Bibliography