Wavelets And Singular Integrals On Curves And Surfaces

Author : Guy David
Publisher : Springer
Page : 119 pages
File Size : 55,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540463771

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Wavelets and Singular Integrals on Curves and Surfaces by Guy David Pdf

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.

Author : Guy David,Albrecht Dold
Publisher : Unknown
Page : 107 pages
File Size : 44,5 Mb
Release : 1991
Category : Maximal functions
ISBN : 7506214849

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Wavelets and Singular Integrals on Curves and Surfaces by Guy David,Albrecht Dold Pdf

Author : Marius Mitrea
Publisher : Springer
Page : 130 pages
File Size : 50,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540483793

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Clifford Wavelets, Singular Integrals, and Hardy Spaces by Marius Mitrea Pdf

The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.

Author : John Ryan
Publisher : CRC Press
Page : 174 pages
File Size : 43,9 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9781351460279

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Clifford Algebras in Analysis and Related Topics by John Ryan Pdf

This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.

Author : Marcin Bownik
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 49,9 Mb
Release : 2003
Category : Hardy spaces
ISBN : 9780821833261

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Anisotropic Hardy Spaces and Wavelets by Marcin Bownik Pdf

Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.

Author : Ingrid Daubechies
Publisher : American Mathematical Soc.
Page : 205 pages
File Size : 55,8 Mb
Release : 2016-04-28
Category : Electronic
ISBN : 9781470429201

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Different Perspectives on Wavelets by Ingrid Daubechies Pdf

The wavelet transform can be seen as a synthesis of ideas that have emerged since the 1960s in mathematics, physics, and electrical engineering. The basic idea is to use a family of ``building blocks'' to represent in an efficient way the object at hand, be it a function, an operator, a signal, or an image. The building blocks themselves come in different ``sizes'' which can describe different features with different resolutions. The papers in this book attempt to give some theoretical and technical shape to this intuitive picture of wavelets and their uses. The papers collected here were prepared for an AMS Short Course on Wavelets and Applications, held at the Joint Mathematics Meetings in San Antonio in January 1993. Here readers will find general background on wavelets as well as more detailed views of specific techniques and applications. With contributions by some of the top experts in the field, this book provides an excellent introduction to this important and growing area of research.

Author : Efi Foufoula-Georgiou,Praveen Kumar
Publisher : Elsevier
Page : 373 pages
File Size : 42,5 Mb
Release : 2014-06-28
Category : Science
ISBN : 9780080520872

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Wavelets in Geophysics by Efi Foufoula-Georgiou,Praveen Kumar Pdf

Applications of wavelet analysis to the geophysical sciences grew from Jean Morlet's work on seismic signals in the 1980s. Used to detect signals against noise, wavelet analysis excels for transients or for spatiallylocalized phenomena. In this fourth volume in the renown WAVELET ANALYSIS AND ITS APPLICATIONS Series, Efi Foufoula-Georgiou and Praveen Kumar begin with a self-contained overview of the nature, power, and scope of wavelet transforms. The eleven originalpapers that follow in this edited treatise show how geophysical researchers are using wavelets to analyze such diverse phenomena as intermittent atmospheric turbulence, seafloor bathymetry, marine and other seismic data, and flow in aquifiers. Wavelets in Geophysics will make informative reading for geophysicists seeking an up-to-date account of how these tools are being used as well as for wavelet researchers searching for ideas for applications, or even new points of departure. Includes twelve original papers written by experts in the geophysical sciences Provides a self-contained overview of the nature, power, and scope of wavelet transforms Presents applications of wavelets to geophysical phenomena such as: The sharp events of seismic data, Long memory processes, such as fluctuation in the level of the Nile, A structure preserving decomposition of turbulence signals

Author : S.P. Singh
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401585774

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Approximation Theory, Wavelets and Applications by S.P. Singh Pdf

Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.

Author : Barbara Burke Hubbard
Publisher : CRC Press
Page : 352 pages
File Size : 51,9 Mb
Release : 1998-05-30
Category : Mathematics
ISBN : 9781439864555

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The World According to Wavelets by Barbara Burke Hubbard Pdf

This best-selling book introduces a broad audience including scientists and engineers working in a variety of fields as well as mathematicians from other subspecialties to one of the most active new areas of applied mathematics and the story of its discovery and development. Organized in "hypertext fashion," the book tells a story of scientific dis

Author : Yves Meyer,Ronald Coifman
Publisher : Cambridge University Press
Page : 340 pages
File Size : 52,6 Mb
Release : 1997
Category : Mathematics
ISBN : 0521794730

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Wavelets by Yves Meyer,Ronald Coifman Pdf

A classic exposition of the theory of wavelets from two of the subject's leading experts.

Author : Guy David,Stephen Semmes
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 49,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821815373

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Analysis of and on Uniformly Rectifiable Sets by Guy David,Stephen Semmes Pdf

The notion of uniform rectifiability of sets (in a Euclidean space), which emerged only recently, can be viewed in several different ways. It can be viewed as a quantitative and scale-invariant substitute for the classical notion of rectifiability; as the answer (sometimes only conjecturally) to certain geometric questions in complex and harmonic analysis; as a condition which ensures the parametrizability of a given set, with estimates, but with some holes and self-intersections allowed; and as an achievable baseline for information about the structure of a set. This book is about understanding uniform rectifiability of a given set in terms of the approximate behavior of the set at most locations and scales. In addition to being the only general reference available on uniform rectifiability, this book also poses many open problems, some of which are quite basic.

Author : T. H. Koornwinder
Publisher : World Scientific
Page : 244 pages
File Size : 41,7 Mb
Release : 1993-01-01
Category : Science
ISBN : 9810224869

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Wavelets by T. H. Koornwinder Pdf

Nowadays, some knowledge of wavelets is almost mandatory for mathematicians, physicists and electrical engineers. The emphasis in this volume, based on an intensive course on Wavelets given at CWI, Amsterdam, is on the affine case. The first part presents a concise introduction of the underlying theory to the uninitiated reader. The second part gives applications in various areas. Some of the contributions here are a fresh exposition of earlier work by others, while other papers contain new results by the authors. The areas are so diverse as seismic processing, quadrature formulae, and wavelet bases adapted to inhomogeneous cases.

Author : Yves Meyer,Sylvie Roques
Publisher : Atlantica Séguier Frontières
Page : 808 pages
File Size : 52,9 Mb
Release : 1993
Category : Wavelets
ISBN : 2863321307

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Progress in Wavelet Analysis and Applications by Yves Meyer,Sylvie Roques Pdf

Author : Guy David
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 51,9 Mb
Release : 2006-03-10
Category : Mathematics
ISBN : 9783764373023

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Singular Sets of Minimizers for the Mumford-Shah Functional by Guy David Pdf

The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. It is largely self-contained, and should be accessible to graduate students in analysis. The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way.

Author : Yves Meyer
Publisher : Cambridge University Press
Page : 248 pages
File Size : 51,7 Mb
Release : 1992
Category : Mathematics
ISBN : 0521458692

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Wavelets and Operators: Volume 1 by Yves Meyer Pdf

The definite mathematical treatment of this important area, written by one of the founders of the field.