Advertisement

Difference Spaces and Invariant Linear Forms

  • Authors
  • Rodney┬áNillsen

Part of the Lecture Notes in Mathematics book series (LNM, volume 1586)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Rodney Nillsen
    Pages 1-8
  3. Rodney Nillsen
    Pages 9-43
  4. Rodney Nillsen
    Pages 44-117
  5. Rodney Nillsen
    Pages 152-174
  6. Back Matter
    Pages 175-188

About this book

Introduction

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.

Keywords

Analysis Differential Operators Harmonie Hilbert space Invariant Linear Forms

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073511
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58323-3
  • Online ISBN 978-3-540-48652-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site