Wavelets and Singular Integrals on Curves and Surfaces

  • Authors
  • Guy¬†David

Part of the Lecture Notes in Mathematics book series (LNM, volume 1465)

Table of contents

  1. Front Matter
    Pages I-X
  2. Guy David
    Pages 1-25
  3. Guy David
    Pages 26-54
  4. Back Matter
    Pages 93-109

About this book

Introduction

Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.

Keywords

Funktionenraum Singular integral calderon-zygmund operators harmonic analysis partielle Differentialgleichungen signal analysis singular integrals wavelets

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0091544
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-53902-5
  • Online ISBN 978-3-540-46377-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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