Clifford Wavelets Singular Integrals And Hardy Spaces
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Clifford Wavelets Singular Integrals And Hardy Spaces
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Author : Marius Mitrea
language : en
Publisher: Springer
Release Date : 2006-11-15
Clifford Wavelets Singular Integrals And Hardy Spaces written by Marius Mitrea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Clifford Wavelets Singular Integrals And Hardy Spaces
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Author : Marius Mitrea
language : en
Publisher: Springer
Release Date : 1994-04-28
Clifford Wavelets Singular Integrals And Hardy Spaces written by Marius Mitrea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-28 with Mathematics categories.
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.
Singular Integrals And Fourier Theory On Lipschitz Boundaries
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Author : Tao Qian
language : en
Publisher: Springer
Release Date : 2019-03-20
Singular Integrals And Fourier Theory On Lipschitz Boundaries written by Tao Qian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.
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.
Clifford Algebras And Their Applications In Mathematical Physics
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Author : Rafał Abłamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Clifford Algebras And Their Applications In Mathematical Physics written by Rafał Abłamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The second part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. from applications such as complex-distance potential theory, supersymmetry, and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications, to mathematical physics and Schwarzian derivatives in Euclidean space. Among the mathematical topics examined are generalized Dirac operators, holonomy groups, monogenic and hypermonogenic functions and their derivatives, quaternionic Beltrami equations, Fourier theory under Mobius transformations, Cauchy-Reimann operators, and Cauchy type integrals.
Lectures On Clifford Geometric Algebras And Applications
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Author : Rafal Ablamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Lectures On Clifford Geometric Algebras And Applications written by Rafal Ablamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
Clifford Algebras And Their Applications In Mathematical Physics
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Author : John Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Clifford Algebras And Their Applications In Mathematical Physics written by John Ryan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Operator Theory For Complex And Hypercomplex Analysis
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Author : Enrique Ramírez de Arellano
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Operator Theory For Complex And Hypercomplex Analysis written by Enrique Ramírez de Arellano and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman opertors, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure opertor theory, and is influential and beneficial for important areas of analysis. Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference "Operator Theory and Complex and Hypercomplex Analysis", held in Decenber 1994 in Mexico City.
Clifford Algebras In Analysis And Related Topics
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Author : John Ryan
language : en
Publisher: CRC Press
Release Date : 2018-03-09
Clifford Algebras In Analysis And Related Topics written by John Ryan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Mathematics categories.
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.
The Hodge Laplacian
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Author : Dorina Mitrea
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-10-10
The Hodge Laplacian written by Dorina Mitrea and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-10 with Mathematics categories.
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains. Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents: Preface Introduction and Statement of Main Results Geometric Concepts and Tools Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism Additional Results and Applications Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis Bibliography Index
Nonlinear Potential Theory And Weighted Sobolev Spaces
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Author : Bengt O. Turesson
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-06-21
Nonlinear Potential Theory And Weighted Sobolev Spaces written by Bengt O. Turesson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-21 with Mathematics categories.
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.