Wavelets and Singular Integrals on Curves and Surfaces. 1st ed. 1991

種類:

電子ブック

責任表示:

by Guy David

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991

著者名:

• David, Guy.
• SpringerLink (Online service)

シリーズ名:

Nankai Institute of Mathematics, Tianjin, P.R. China ; 1465

ISBN:

9783540463771 [3540463771]    

注記:

Wavelets -- Singular integral operators -- Singular integrals on curves and surfaces.
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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