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From the reviews of the first edition: "This lovely book is intended as a primer in harmonic analysis at the undergraduate level. All the central concepts of harmonic analysis are introduced using Riemann integral and metric spaces only. The exercises at the end of each chapter are interesting and challenging..." Sanjiv Kumar Gupta for MathSciNet "... In this well-written textbook the central concepts of Harmonic Analysis are explained in an enjoyable way, while using very little technical background. Quite surprisingly this approach works. It is not an exaggeration that each undergraduate student interested in and each professor teaching Harmonic Analysis will benefit from the streamlined and direct approach of this book." Ferenc Móricz for Acta Scientiarum Mathematicarum This book is a primer in harmonic analysis using an elementary approach. Its first aim is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Secondly, it makes the reader aware of the fact that both, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. There are two new chapters in this new edition. One on distributions will complete the set of real variable methods introduced in the first part. The other on the Heisenberg Group provides an example of a group that is neither compact nor abelian, yet is simple enough to easily deduce the Plancherel Theorem. Professor Deitmar is Professor of Mathematics at the University of T"ubingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. In his leisure time he enjoys hiking in the mountains and practicing Aikido.

Harmonic analysis. --- Analyse harmonique --- Harmonic analysis --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Topological groups. --- Lie groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Topology. --- Functional Analysis. --- Abstract Harmonic Analysis. --- Topological Groups, Lie Groups. --- Analysis. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Topological Groups. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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Topological groups. Lie groups --- Mathematical analysis --- analyse (wiskunde) --- topologie (wiskunde)

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In diesem Lehrbuch wird der Stoff einer dreisemestrigen Anfängervorlesung zur Analysis in einer bisher nicht gekannten Prägnanz dargeboten, ohne dass die Verständlichkeit der sprachlichen Darstellung dadurch vernachlässigt wird. Das Buch bietet so eine umfassende Vollständigkeit des Stoffes, die ihres Gleichen sucht. Die Inhalte decken die in einer heutigen Bachelor-Vorlesung zur Analysis üblichen Themen ab: Ein- und mehrdimensionale Differential- und Integralrechnung, gewöhnliche Differentialgleichungen, Maß- und Integrationstheorie, Differentialformen und der Satz von Stokes. Darüber hinaus sind Kapitel über metrische Räume und allgemeine mengentheoretische Topologie enthalten. Der Autor Prof. Dr. Anton Deitmar, Universität Tübingen, Mathematisches Institut.

Mathematical analysis. --- Analysis (Mathematics). --- Analysis.

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The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, or independently, if the students already have a modest knowledge of Fourier Analysis. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in A First Course in Harmonic Analysis. Using Pontryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and its applications to theory in number theory and the theory of wavelets. Knowledge of set theoretic topology, Lebesgue integration, and functional analysis on an introductory level will be required in the body of the book. For the convenience of the reader, all necessary ingredients from these areas have been included in the appendices. Professor Deitmar is Professor of Mathematics at the University of Tübingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. Professor Echterhoff is Professor of Mathematics and Computer Science at the University of Münster, Germany.

Electronic books. -- local. --- Harmonic analysis. --- Mathematical analysis. --- Harmonic analysis --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Fourier analysis. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analysis, Fourier --- Math --- Science

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Harmonic analysis. Fourier analysis --- Mathematical analysis --- Fourieranalyse --- analyse (wiskunde) --- Fourierreeksen --- mathematische modellen