Principles of Harmonic Analysis (repost)
Principles of Harmonic Analysis (Universitext) by Anton Deitmar and Siegfried Echterhoff
English | 2008-11-21 | ISBN: 0387854681 | 336 pages | PDF | 2,3 mb
English | 2008-11-21 | ISBN: 0387854681 | 336 pages | PDF | 2,3 mb
The book is written for graduate students who have read the first book and like to see the proofs which were not given there and/or want to see the full extent of the theory. On the other hand it can be read independently from the first one, only a modest knowledge on Fourier series/tranform is required to understand the examples.
This book fills a major gap in the textbook literature, as a full proof of Pontryagin Duality and Plancherel Theorem is hard to come by. It is usually given in books that focus on C*-algebras and thus carry too much technical overload for the reader who only wants these basic results of Harmonic Analysis. Other proofs use the structure theory which carries the reader away in a different direction. Here the authors consider the Banach-algebra approach more elegant and enlighting. They provide a streamlined approach that reaches the main results directly, and they also give the generalizations to the non-Abelian case. Another main pillar of Harmonic analysis is the Poisson Summation Formula. We give its generalization to LCA-groups.