ABSTRACT

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

chapter 1|34 pages

Banach Algebras and Spectral Theory

chapter 2|38 pages

Locally Compact Groups

chapter 3|22 pages

Basic Representation Theory

chapter 4|40 pages

Analysis on Locally Compact Abelian Groups

chapter 5|28 pages

Analysis on Compact Groups

chapter 6|60 pages

Induced Representations

chapter 7|50 pages

Further Topics in Representation Theory

chapter 1|3 pages

A Hilbert Space Miscellany

chapter 2|3 pages

Trace-Class and Hilbert-Schmidt Operators

chapter 3|5 pages

Tensor Products of Hilbert Spaces

chapter 4|5 pages

Vector-Valued Integrals