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.

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

• Front Matter
• Wavelets
• Singular integral operators
• Singular integrals on curves and surfaces
• Back Matter

N/A

Book Title
Wavelets and Singular Integrals on Curves and Surfaces

Authors
Guy David

Series Title
Lecture Notes in Mathematics

DOI
https://doi.org/10.1007/BFb0091544

Softcover ISBN
978-3-540-53902-5
Published: 10 July 1991

eBook ISBN
978-3-540-46377-1
Published: 14 November 2006

Series ISSN
0075-8434

Series E-ISSN
1617-9692

Edition Number
1

Number of Pages
X, 110

Topics
Applications of Mathematics, Analysis, Functional Analysis, Topological Groups, Lie Groups, Real Functions