Beschreibung:
The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, or independently, if the students already have a modest knowledge of Fourier Analysis. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in A First Course in Harmonic Analysis. Using Pontryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and its applications to theory in number theory and the theory of wavelets.
Haar Integration.- Banach Algebras.- Duality for Abelian Groups.- The Structure of LCA-Groups.- Operators on Hilbert Spaces.- Representations.- Compact Groups.- Direct Integrals.- The Selberg Trace Formula.- The Heisenberg Group.- SL2(?).- Wavelets.