The series de Gruyter Studies in Mathematics was founded in 1982 by the late Professor Heinz Bauer and Professor Peter Gabriel.

The series publishes monographs and textbooks in mathematics and its applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.

Each volume undergoes peer review using a double-blind reviewing process

This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed.

This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space.

From the contents

• Fourier series
• Fourier integrals
• Locally compact groups
• Haar measures
• Harmonic analysis on locally compact abelian groups
• Theory and examples of Gelfand pairs
• Theory and examples of generalized Gelfand pairs

Autorentext

Gerrit van Dijk, Leiden University, Netherlands