Wavelets and Singular Integrals on Curves and Surfaces

1991
ISBN: 978-3-540-53902-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 110 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 195 g

Reihe: Nankai Institute of Mathematics, Tianjin, P.R. China

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.

Zielgruppe

Research

Autoren/Hrsg.

David, Guy

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

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