Banach Algebras and Spectral Theory
Banach Algebras: Basic Concepts
Gelfand Theory
Nonunital Banach Algebras
The Spectral Theorem
Spectral Theory of *-Representations
Von Neumann Algebras
Notes and References
Locally Compact Groups
Topological Groups
Haar Measure
Interlude: Some Technicalities
The Modular Function
Convolutions
Homogeneous Spaces
Notes and References
Basic Representation Theory
Unitary Representations
Representations of a Group and Its Group Algebra
Functions of Positive Type
Notes and References
Analysis on Locally Compact Abelian Groups
The Dual Group
The Fourier Transform
The Pontrjagin Duality Theorem
Representations of Locally Compact Abelian Groups
Closed Ideals in L1(G)
Spectral Synthesis
The Bohr Compactification
Notes and References
Analysis on Compact Groups
Representations of Compact Groups
The Peter-Weyl Theorem
Fourier Analysis on Compact Groups
Examples
Notes and References
Induced Representations
The Inducing Construction
The Frobenius Reciprocity Theorem
Pseudomeasures and Induction in Stages
Systems of Imprimitivity
The Imprimitivity Theorem
Introduction to the Mackey Machine
Examples: The Classics
More Examples, Good and Bad
Notes and References
Further Topics in Representation Theory
The Group C* Algebra
The Structure of the Dual Space
Tensor Products of Representations
Direct Integral Decompositions
The Plancherel Theorem
Examples
Appendices
A Hilbert Space Miscellany
Trace-Class and Hilbert-Schmidt Operators
Tensor Products of Hilbert Spaces
Vector-Valued Integrals
Biography
Gerald B. Folland received his Ph.D in mathematics from Princeton University, New Jersey, USA in 1971. After two years at the Courant Institute of Mathematical Sciences, New York, USA, he joined the faculty of the University of Washington, Seattle, USA, where he is now professor emeritus of mathematics. He has written a number of research and expository articles on harmonic analysis and its applications, and he is the author of eleven textbooks and research monographs.
Praise for the Previous Edition
"This delightful book fills a long-standing gap in the literature on abstract harmonic analysis. … To the reviewer's knowledge, no one existing book contains all of the topics that are treated in this one. … [The author's] respect for the subject shows on every hand…through his careful writing style, which is concise, yet simple and elegant. The reviewer would encourage anyone with an interest in harmonic analysis to have this book in his or her personal library. … a fine book that the reviewer would have been proud to write."
—Robert S. Doran in Mathematical Reviews®, Issue 98c
