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.
Readership
Graduate students and researchers interested in
abstract harmonic analysis, Banach algebras, and operator
spaces.