Wavelets And Singular Integrals On Curves And Surfaces
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Author |
: Guy David |
Publisher |
: Springer |
Total Pages |
: 119 |
Release |
: 2006-11-14 |
ISBN-10 |
: 9783540463771 |
ISBN-13 |
: 3540463771 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Wavelets and Singular Integrals on Curves and Surfaces by : Guy David
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 |
Publisher |
: |
Total Pages |
: 107 |
Release |
: 1991 |
ISBN-10 |
: 7506214849 |
ISBN-13 |
: 9787506214841 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Wavelets and Singular Integrals on Curves and Surfaces by : Guy David
Author |
: Tao Qian |
Publisher |
: Springer |
Total Pages |
: 315 |
Release |
: 2019-03-20 |
ISBN-10 |
: 9789811365003 |
ISBN-13 |
: 9811365008 |
Rating |
: 4/5 (03 Downloads) |
Synopsis Singular Integrals and Fourier Theory on Lipschitz Boundaries by : Tao Qian
The main purpose of this book is to provide a detailed and comprehensive survey of the theory of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has been developed since the 1980s. The subject of singular integrals and the related Fourier multipliers on Lipschitz curves and surfaces has an extensive background in harmonic analysis and partial differential equations. The book elaborates on the basic framework, the Fourier methodology, and the main results in various contexts, especially addressing the following topics: singular integral operators with holomorphic kernels, fractional integral and differential operators with holomorphic kernels, holomorphic and monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and the high-dimensional Fueter mapping theorem with applications. The book offers a valuable resource for all graduate students and researchers interested in singular integrals and Fourier multipliers.
Author |
: Marius Mitrea |
Publisher |
: |
Total Pages |
: 136 |
Release |
: 2014-01-15 |
ISBN-10 |
: 3662212935 |
ISBN-13 |
: 9783662212936 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Clifford Wavelets, Singular Integrals, and Hardy Spaces by : Marius Mitrea
Author |
: Andreas Seeger |
Publisher |
: |
Total Pages |
: 13 |
Release |
: 1995 |
ISBN-10 |
: OCLC:223557443 |
ISBN-13 |
: |
Rating |
: 4/5 (43 Downloads) |
Synopsis Classes of Singular Integrals Along Curves and Surfaces by : Andreas Seeger
Author |
: Marius Mitrea |
Publisher |
: Springer |
Total Pages |
: 130 |
Release |
: 2006-11-15 |
ISBN-10 |
: 9783540483793 |
ISBN-13 |
: 3540483799 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Clifford Wavelets, Singular Integrals, and Hardy Spaces by : Marius Mitrea
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 |
: Juan José Marín |
Publisher |
: Springer Nature |
Total Pages |
: 605 |
Release |
: 2022-09-29 |
ISBN-10 |
: 9783031082344 |
ISBN-13 |
: 3031082346 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Singular Integral Operators, Quantitative Flatness, and Boundary Problems by : Juan José Marín
This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.
Author |
: Luca Capogna |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 170 |
Release |
: 2005 |
ISBN-10 |
: 9780821827284 |
ISBN-13 |
: 0821827286 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Harmonic Measure by : Luca Capogna
Recent developments in geometric measure theory and harmonic analysis have led to new and deep results concerning the regularity of the support of measures which behave "asymptotically" (for balls of small radius) as the Euclidean volume. A striking feature of these results is that they actually characterize flatness of the support in terms of the asymptotic behavior of the measure. Such characterizations have led to important new progress in the study of harmonic measure fornon-smooth domains. This volume provides an up-to-date overview and an introduction to the research literature in this area. The presentation follows a series of five lectures given by Carlos Kenig at the 2000 Arkansas Spring Lecture Series. The original lectures have been expanded and updated to reflectthe rapid progress in this field. A chapter on the planar case has been added to provide a historical perspective. Additional background has been included to make the material accessible to advanced graduate students and researchers in harmonic analysis and geometric measure theory.
Author |
: Xavier Tolsa |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 402 |
Release |
: 2013-12-16 |
ISBN-10 |
: 9783319005966 |
ISBN-13 |
: 3319005960 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory by : Xavier Tolsa
This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers.
Author |
: Guy David |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 146 |
Release |
: 2000 |
ISBN-10 |
: 9780821820483 |
ISBN-13 |
: 0821820486 |
Rating |
: 4/5 (83 Downloads) |
Synopsis Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension by : Guy David
This book is intended for graduate students and research mathematicians interested in calculus of variations and optimal control; optimization.