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Essays in Commutative Harmonic Analysis

  • Colin C. Graham
  • O. Carruth McGehee

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 238)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Colin C. Graham, O. Carruth McGehee
    Pages 1-47
  3. Colin C. Graham, O. Carruth McGehee
    Pages 48-67
  4. Colin C. Graham, O. Carruth McGehee
    Pages 68-90
  5. Colin C. Graham, O. Carruth McGehee
    Pages 91-121
  6. Colin C. Graham, O. Carruth McGehee
    Pages 122-137
  7. Colin C. Graham, O. Carruth McGehee
    Pages 138-195
  8. Colin C. Graham, O. Carruth McGehee
    Pages 196-227
  9. Colin C. Graham, O. Carruth McGehee
    Pages 228-250
  10. Colin C. Graham, O. Carruth McGehee
    Pages 251-280
  11. Colin C. Graham, O. Carruth McGehee
    Pages 281-307
  12. Colin C. Graham, O. Carruth McGehee
    Pages 308-361
  13. Colin C. Graham, O. Carruth McGehee
    Pages 362-401
  14. Colin C. Graham, O. Carruth McGehee
    Pages 402-423
  15. Back Matter
    Pages 425-466

About this book

Introduction

This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact abelian group, and studied in the light of the Fourier transform. The emphasis is on the objects themselves, and on the structure-in-detail of the spaces and algebras. A mathematician needs to know only a little about Fourier analysis on the commutative groups, and then may go many ways within the large subject of harmonic analysis-into the beautiful theory of Lie group representations, for example. But this book represents the tendency to linger on the line, and the other abelian groups, and to keep asking questions about the structures thereupon. That tendency, pursued since the early days of analysis, has defined a field of study that can boast of some impressive results, and in which there still remain unanswered questions of compelling interest. We were influenced early in our careers by the mathematicians Jean-Pierre Kahane, Yitzhak Katznelson, Paul Malliavin, Yves Meyer, Joseph Taylor, and Nicholas Varopoulos. They are among the many who have made the field a productive meeting ground of probabilistic methods, number theory, diophantine approximation, and functional analysis. Since the academic year 1967-1968, when we were visitors in Paris and Orsay, the field has continued to see interesting developments. Let us name a few. Sam Drury and Nicholas Varopoulos solved the union problem for Helson sets, by proving a remarkable theorem (2.1.3) which has surely not seen its last use.

Keywords

Algebra Derivation Division Finite Harmonische Analyse Invariant Morphism calculus commutative property function proof theorem

Authors and affiliations

  • Colin C. Graham
    • 1
  • O. Carruth McGehee
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-9976-9
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-9978-3
  • Online ISBN 978-1-4612-9976-9
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site