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Wavelets and Singular Integrals on Curves and Surfaces

  • Book
  • © 1991

Overview

Authors:
  1. Guy David
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1465)

Part of the book sub series: Nankai Institute of Mathematics, Tianjin, P.R. China (2803)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-X
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  2. Wavelets

    • Guy David
    Pages 1-25

  3. Singular integral operators

    • Guy David
    Pages 26-54

  4. Singular integrals on curves and surfaces

    • Guy David
    Pages 55-92

  5. Back Matter

    Pages 93-109
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Keywords

About this book

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.

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