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Essays in Commutative Harmonic Analysis

  • Book
  • © 1979

Overview

Authors:
  1. Colin C. Graham

    1. Department of Mathematics, Northwestern University, Evanston, USA

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    You can also search for this author in PubMed   Google Scholar

  2. O. Carruth McGehee

    1. Department of Mathematics, Louisiana State University, Baton Rouge, USA

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxi
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  2. The Behavior of Transforms

    • Colin C. Graham, O. Carruth McGehee
    Pages 1-47

  3. A Proof That the Union of Two Helson Sets Is a Helson Set

    • Colin C. Graham, O. Carruth McGehee
    Pages 48-67

  4. Harmonic Synthesis

    • Colin C. Graham, O. Carruth McGehee
    Pages 68-90

  5. Sets of Uniqueness, Sets of Multiplicity

    • Colin C. Graham, O. Carruth McGehee
    Pages 91-121

  6. A Brief Introduction to Convolution Measure Algebras

    • Colin C. Graham, O. Carruth McGehee
    Pages 122-137

  7. Independent Power Measures

    • Colin C. Graham, O. Carruth McGehee
    Pages 138-195

  8. Riesz Products

    • Colin C. Graham, O. Carruth McGehee
    Pages 196-227

  9. The Šilov Boundary, Symmetric Ideals, and Gleason Parts of ΔM(G)

    • Colin C. Graham, O. Carruth McGehee
    Pages 228-250

  10. The Wiener-Lévy Theorem and Some of Its Converses

    • Colin C. Graham, O. Carruth McGehee
    Pages 251-280

  11. The Multiplier Algebras M p (Γ), and the Theorem of Zafran

    • Colin C. Graham, O. Carruth McGehee
    Pages 281-307

  12. Tensor Algebras and Harmonic Analysis

    • Colin C. Graham, O. Carruth McGehee
    Pages 308-361

  13. Tilde Algebras

    • Colin C. Graham, O. Carruth McGehee
    Pages 362-401

  14. Unsolved Problems

    • Colin C. Graham, O. Carruth McGehee
    Pages 402-423

  15. Back Matter

    Pages 425-466
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Northwestern University, Evanston, USA

    Colin C. Graham

  • Department of Mathematics, Louisiana State University, Baton Rouge, USA

    O. Carruth McGehee

Bibliographic Information

  • Book Title: Essays in Commutative Harmonic Analysis

  • Authors: Colin C. Graham, O. Carruth McGehee

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-1-4612-9976-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1979

  • Softcover ISBN: 978-1-4612-9978-3Published: 09 November 2011

  • eBook ISBN: 978-1-4612-9976-9Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: 464

  • Topics: Analysis

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