Topics In Clifford Analysis

Topics In Clifford Analysis Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Topics In Clifford Analysis book. This book definitely worth reading, it is an incredibly well-written.

Topics in Clifford Analysis

Swanhild Bernstein
Topics in Clifford Analysis Book PDF

Author : Swanhild Bernstein
Publisher : Springer Nature
Page : 503 pages
File Size : 53,8 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9783030238544

Get Book

Topics in Clifford Analysis by Swanhild Bernstein Pdf

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.

Clifford Algebras in Analysis and Related Topics

John Ryan
Clifford Algebras in Analysis and Related Topics Book PDF

Author : John Ryan
Publisher : CRC Press
Page : 174 pages
File Size : 40,7 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9781351460279

Get Book

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.

Clifford Analysis and Related Topics

Paula Cerejeiras,Craig A. Nolder,John Ryan,Carmen Judith Vanegas Espinoza
Clifford Analysis and Related Topics Book PDF

Author : Paula Cerejeiras,Craig A. Nolder,John Ryan,Carmen Judith Vanegas Espinoza
Publisher : Springer
Page : 152 pages
File Size : 49,6 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783030000493

Get Book

Clifford Analysis and Related Topics by Paula Cerejeiras,Craig A. Nolder,John Ryan,Carmen Judith Vanegas Espinoza Pdf

This book, intended to commemorate the work of Paul Dirac, highlights new developments in the main directions of Clifford analysis. Just as complex analysis is based on the algebra of the complex numbers, Clifford analysis is based on the geometric Clifford algebras. Many methods and theorems from complex analysis generalize to higher dimensions in various ways. However, many new features emerge in the process, and much of this work is still in its infancy. Some of the leading mathematicians working in this field have contributed to this book in conjunction with “Clifford Analysis and Related Topics: a conference in honor of Paul A.M. Dirac,” which was held at Florida State University, Tallahassee, on December 15-17, 2014. The content reflects talks given at the conference, as well as contributions from mathematicians who were invited but were unable to attend. Hence much of the mathematics presented here is not only highly topical, but also cannot be found elsewhere in print. Given its scope, the book will be of interest to mathematicians and physicists working in these areas, as well as students seeking to catch up on the latest developments.

Clifford Analysis and Its Applications

F. Brackx,John Stephen roy Chisholm,V. Soucek
Clifford Analysis and Its Applications Book PDF

Author : F. Brackx,John Stephen roy Chisholm,V. Soucek
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 55,7 Mb
Release : 2001-07-31
Category : Mathematics
ISBN : 0792370449

Get Book

Clifford Analysis and Its Applications by F. Brackx,John Stephen roy Chisholm,V. Soucek Pdf

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

Clifford Algebras and Dirac Operators in Harmonic Analysis

John E. Gilbert,Margaret Anne Marie Murray
Clifford Algebras and Dirac Operators in Harmonic Analysis Book PDF

Author : John E. Gilbert,Margaret Anne Marie Murray
Publisher : Cambridge University Press
Page : 346 pages
File Size : 52,5 Mb
Release : 1991-07-26
Category : Mathematics
ISBN : 0521346541

Get Book

Clifford Algebras and Dirac Operators in Harmonic Analysis by John E. Gilbert,Margaret Anne Marie Murray Pdf

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Introduction to Clifford Analysis

Johan Ceballos
Introduction to Clifford Analysis Book PDF

Author : Johan Ceballos
Publisher : Nova Science Publishers
Page : 182 pages
File Size : 46,6 Mb
Release : 2020
Category : Mathematics
ISBN : 1536186643

Get Book

Introduction to Clifford Analysis by Johan Ceballos Pdf

This book pursues to exhibit how we can construct a Clifford type algebra from the classical one. The basic idea of these lecture notes is to show how to calculate fundamental solutions to either first-order differential operators of the form D=∑_(i=0)^n▒〖e_i δ_i〗or second-order elliptic differential operators ̄D D, both with constant coefficients or combinations of this kind of operators. After considering in detail how to find the fundamental solution we study the problem of integral representations in a classical Clifford algebra and in a dependent-parameter Clifford algebra which generalizes the classical one. We also propose a basic method to extend the order of the operator, for instance D^n,n∈N and how to produce integral representations for higher order operators and mixtures of them. Although the Clifford algebras have produced many applications concerning boundary value problems, initial value problems, mathematical physics, quantum chemistry, among others; in this book we do not discuss these topics as they are better discussed in other courses. Researchers and practitioners will find this book very useful as a source book.The reader is expected to have basic knowledge of partial differential equations and complex analysis. When planning and writing these lecture notes, we had in mind that they would be used as a resource by mathematics students interested in understanding how we can combine partial differential equations and Clifford analysis to find integral representations. This in turn would allow them to solve boundary value problems and initial value problems. To this end, proofs have been described in rigorous detail and we have included numerous worked examples. On the other hand, exercises have not been included.

Clifford Algebras

Rafal Ablamowicz
Clifford Algebras Book PDF

Author : Rafal Ablamowicz
Publisher : Springer Science & Business Media
Page : 635 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220442

Get Book

Clifford Algebras by Rafal Ablamowicz Pdf

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

Clifford Analysis and Related Topics

Paula Cerejeiras,Craig Nolder,John Ryan,Carmen Judith Vanegas Espinoza
Clifford Analysis and Related Topics Book PDF

Author : Paula Cerejeiras,Craig Nolder,John Ryan,Carmen Judith Vanegas Espinoza
Publisher : Unknown
Page : 152 pages
File Size : 42,8 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 3030000486

Get Book

Clifford Analysis and Related Topics by Paula Cerejeiras,Craig Nolder,John Ryan,Carmen Judith Vanegas Espinoza Pdf

This book, intended to commemorate the work of Paul Dirac, highlights new developments in the main directions of Clifford analysis. Just as complex analysis is based on the algebra of the complex numbers, Clifford analysis is based on the geometric Clifford algebras. Many methods and theorems from complex analysis generalize to higher dimensions in various ways. However, many new features emerge in the process, and much of this work is still in its infancy. Some of the leading mathematicians working in this field have contributed to this book in conjunction with “Clifford Analysis and Related Topics: a conference in honor of Paul A.M. Dirac,” which was held at Florida State University, Tallahassee, on December 15-17, 2014. The content reflects talks given at the conference, as well as contributions from mathematicians who were invited but were unable to attend. Hence much of the mathematics presented here is not only highly topical, but also cannot be found elsewhere in print. Given its scope, the book will be of interest to mathematicians and physicists working in these areas, as well as students seeking to catch up on the latest developments.--

Clifford Algebras and their Applications in Mathematical Physics

F. Brackx,R. Delanghe,H. Serras
Clifford Algebras and their Applications in Mathematical Physics Book PDF

Author : F. Brackx,R. Delanghe,H. Serras
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401120067

Get Book

Clifford Algebras and their Applications in Mathematical Physics by F. Brackx,R. Delanghe,H. Serras Pdf

This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.

Clifford Analysis and Its Applications

F. Brackx,J.S.R. Chisholm,V. Soucek
Clifford Analysis and Its Applications Book PDF

Author : F. Brackx,J.S.R. Chisholm,V. Soucek
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401008624

Get Book

Clifford Analysis and Its Applications by F. Brackx,J.S.R. Chisholm,V. Soucek Pdf

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

Introduction to Clifford Analysis

Johan Ceballos
Introduction to Clifford Analysis Book PDF

Author : Johan Ceballos
Publisher : Nova Science Publishers
Page : 182 pages
File Size : 48,5 Mb
Release : 2020-10-30
Category : Electronic
ISBN : 1536185337

Get Book

Introduction to Clifford Analysis by Johan Ceballos Pdf

This book pursues to exhibit how we can construct a Clifford type algebra from the classical one. The basic idea of these lecture notes is to show how to calculate fundamental solutions to either first-order differential operators of the form D=∑_(i=0)^n▒〖e_i δ_i〗or second-order elliptic differential operators ̄D D, both with constant coefficients or combinations of this kind of operators. After considering in detail how to find the fundamental solution we study the problem of integral representations in a classical Clifford algebra and in a dependent-parameter Clifford algebra which generalizes the classical one. We also propose a basic method to extend the order of the operator, for instance D^n,n∈N and how to produce integral representations for higher order operators and mixtures of them. Although the Clifford algebras have produced many applications concerning boundary value problems, initial value problems, mathematical physics, quantum chemistry, among others; in this book we do not discuss these topics as they are better discussed in other courses. Researchers and practitioners will find this book very useful as a source book.The reader is expected to have basic knowledge of partial differential equations and complex analysis. When planning and writing these lecture notes, we had in mind that they would be used as a resource by mathematics students interested in understanding how we can combine partial differential equations and Clifford analysis to find integral representations. This in turn would allow them to solve boundary value problems and initial value problems. To this end, proofs have been described in rigorous detail and we have included numerous worked examples. On the other hand, exercises have not been included.

Clifford Algebras and their Applications in Mathematical Physics

Rafał Abłamowicz
Clifford Algebras and their Applications in Mathematical Physics Book PDF

Author : Rafał Abłamowicz
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 47,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0817641831

Get Book

Clifford Algebras and their Applications in Mathematical Physics by Rafał Abłamowicz Pdf

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.

Quaternion and Clifford Fourier Transforms and Wavelets

Eckhard Hitzer,Stephen J. Sangwine
Quaternion and Clifford Fourier Transforms and Wavelets Book PDF

Author : Eckhard Hitzer,Stephen J. Sangwine
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 48,7 Mb
Release : 2013-06-24
Category : Mathematics
ISBN : 9783034806039

Get Book

Quaternion and Clifford Fourier Transforms and Wavelets by Eckhard Hitzer,Stephen J. Sangwine Pdf

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

Clifford Algebras

Rafal Ablamowicz
Clifford Algebras Book PDF

Author : Rafal Ablamowicz
Publisher : Birkhäuser
Page : 626 pages
File Size : 45,7 Mb
Release : 2011-09-30
Category : Mathematics
ISBN : 1461273935

Get Book

Clifford Algebras by Rafal Ablamowicz Pdf

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

Clifford Algebras and Their Applications in Mathematical Physics

Rafal Ablamowicz
Clifford Algebras and Their Applications in Mathematical Physics Book PDF

Author : Rafal Ablamowicz
Publisher : Birkhauser
Page : 496 pages
File Size : 50,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0817641823

Get Book

Clifford Algebras and Their Applications in Mathematical Physics by Rafal Ablamowicz Pdf

The first 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. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.