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Commutative Harmonic Analysis II

Group Methods in Commutative Harmonic Analysis

  • V. P. Havin
  • N. K. Nikolski

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 25)

Table of contents

  1. Front Matter
    Pages I-9
  2. V. P. Havin, N. K. Nikolski
    Pages 10-158
  3. Back Matter
    Pages 299-328

About this book

Introduction

Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop (and still does), conquering new unexpected areas and producing impressive applications to a multitude of problems, old and new, ranging from arithmetic to optics, from geometry to quantum mechanics, not to mention analysis and differential equations. The power of group theoretic ideology is successfully illustrated by this wide range of topics. It is widely understood now that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This volume is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in the present volume can hardly be found in any monograph. This book will be very useful to a wide circle of readers, including mathematicians, theoretical physicists and engineers.

Keywords

Dualitätstheorie Harmonische Analyse calculus duality theory fourier operator harmonic analysis integration locally compact abelian groups lokal kompakte abelsche Gruppen operator translation invariant subspaces translationsinvariante Unterräume

Editors and affiliations

  • V. P. Havin
    • 1
    • 2
  • N. K. Nikolski
    • 3
    • 4
  1. 1.Department of MathematicsSt. Petersburg State UniversitySt. Petersburg, Staryj PeterhofRussia
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  3. 3.Steklov Mathematical InstituteSt. PetersburgRussia
  4. 4.Département de MathématiquesUniversité de Bordeaux ITalence, CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58946-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63800-8
  • Online ISBN 978-3-642-58946-1
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site