TY - BOOK ID - 17198611 TI - Introduction to harmonic analysis and generalized Gelfand pairs PY - 2009 VL - 36 SN - 01790986 SN - 3110220199 9783110220193 9786612714870 3110220202 1282714872 9783110220209 PB - Berlin ; New York : Walter De Gruyter, DB - UniCat KW - Harmonic analysis. KW - Fourier analysis. KW - Analysis, Fourier KW - Analysis (Mathematics) KW - Functions, Potential KW - Potential functions KW - Mathematical analysis KW - Banach algebras KW - Calculus KW - Mathematics KW - Bessel functions KW - Fourier series KW - Harmonic functions KW - Time-series analysis KW - Generalized Gelfand Pairs. KW - Harmonic Analysis. KW - Locally Compact Abelian Groups. UR - https://www.unicat.be/uniCat?func=search&query=sysid:17198611 AB - 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 ER -