Introduction to Harmonic Analysis and Generalized Gelfand Pairs / / Gerrit van Dijk.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Dijk, Gerrit van,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2009]; ©2009
• Year of Publication: 2009
• Language: English
• Series: De Gruyter Studies in Mathematics , 36
• Physical Description: 1 online resource (223 p.)

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

Table of Contents

Frontmatter -- Contents -- 1 Fourier Series -- 2 Fourier Integrals -- 3 Locally Compact Groups -- 4 Haar Measures -- 5 Harmonic Analysis on Locally Compact Abelian Groups -- 6 Classical Theory of Gelfand Pairs -- 7 Examples of Gelfand Pairs -- 8 Theory of Generalized Gelfand Pairs -- 9 Examples of Generalized Gelfand Pairs -- Backmatter