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Difference Spaces and Invariant Linear Forms

  • Book
  • © 1994

Overview

Authors:
  1. Rodney Nillsen
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1586)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    • Rodney Nillsen
    Pages 1-8

  3. General and preparatory results

    • Rodney Nillsen
    Pages 9-43

  4. Multiplication and difference spaces on R n

    • Rodney Nillsen
    Pages 44-117

  5. Applications to differential and singular integral operators

    • Rodney Nillsen
    Pages 118-151

  6. Results for L p spaces on general groups

    • Rodney Nillsen
    Pages 152-174

  7. Back Matter

    Pages 175-188
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Keywords

About this book

Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, e.g., the origin. One aim is to establish connections between these spaces and differential operators, singular integral operators and wavelets. Another aim is to discuss aspects of these ideas which emphasise invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a clear, accessible and unified viewpoint, which emphasises connections with related work.

Bibliographic Information

  • Book Title: Difference Spaces and Invariant Linear Forms

  • Authors: Rodney Nillsen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073511

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58323-3Published: 25 November 1994

  • eBook ISBN: 978-3-540-48652-7Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 192

  • Topics: Analysis, Topological Groups, Lie Groups

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