Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups
About this Title
Eberhard Kaniuth and Anthony To-Ming Lau, University of Alberta, Edmonton, AB, Canada
Publication: Mathematical Surveys and Monographs
Publication Year: 2018; Volume 231
ISBNs: 978-0-8218-5365-8 (print); 978-1-4704-4768-7 (online)
MathSciNet review: MR3821506
MSC: Primary 45-02; Secondary 22-02, 43A10, 43A25, 43A30, 46-02
The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists.
Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.
Graduate students and researchers interested in abstract harmonic analysis, Banach algebras, and operator spaces.
Table of Contents
- Basic theory of Fourier and Fourier-Stieltjes algebras
- Miscellaneous further topics
- Amenability properties of $A(G)$ and $B(G)$
- Multiplier algebras of Fourier algebras
- Spectral synthesis and ideal theory
- Extension and separation properties of positive definite functions