Hypercomplex Analysis And Applications

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Hypercomplex Analysis and Applications

Irene Sabadini,Franciscus Sommen
Hypercomplex Analysis and Applications Book PDF

Author : Irene Sabadini,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 40,5 Mb
Release : 2010-12-21
Category : Mathematics
ISBN : 9783034602464

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Hypercomplex Analysis and Applications by Irene Sabadini,Franciscus Sommen Pdf

The purpose of the volume is to bring forward recent trends of research in hypercomplex analysis. The list of contributors includes first rate mathematicians and young researchers working on several different aspects in quaternionic and Clifford analysis. Besides original research papers, there are papers providing the state-of-the-art of a specific topic, sometimes containing interdisciplinary fields. The intended audience includes researchers, PhD students, postgraduate students who are interested in the field and in possible connection between hypercomplex analysis and other disciplines, including mathematical analysis, mathematical physics, algebra.

Hypercomplex Analysis: New Perspectives and Applications

Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen
Hypercomplex Analysis New Perspectives and Applications Book PDF

Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen
Publisher : Springer
Page : 227 pages
File Size : 41,7 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783319087719

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Hypercomplex Analysis: New Perspectives and Applications by Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen Pdf

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.

Modern Trends in Hypercomplex Analysis

Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen
Modern Trends in Hypercomplex Analysis Book PDF

Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen
Publisher : Birkhäuser
Page : 310 pages
File Size : 46,5 Mb
Release : 2016-11-21
Category : Mathematics
ISBN : 9783319425290

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Modern Trends in Hypercomplex Analysis by Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen Pdf

This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications.

Hypercomplex Analysis

Irene Sabadini,Michael Shapiro,Franciscus Sommen
Hypercomplex Analysis Book PDF

Author : Irene Sabadini,Michael Shapiro,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 53,8 Mb
Release : 2009-04-21
Category : Mathematics
ISBN : 9783764398934

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Hypercomplex Analysis by Irene Sabadini,Michael Shapiro,Franciscus Sommen Pdf

Contains selected papers from the ISAAC conference 2007 and invited contributions. This book covers various topics that represent the main streams of research in hypercomplex analysis as well as the expository articles. It is suitable for researchers and postgraduate students in various areas of mathematical analysis.

Advances in Hypercomplex Analysis

Graziano Gentili,Irene Sabadini,Michael Shapiro,Franciscus Sommen,Daniele C. Struppa
Advances in Hypercomplex Analysis Book PDF

Author : Graziano Gentili,Irene Sabadini,Michael Shapiro,Franciscus Sommen,Daniele C. Struppa
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 41,8 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9788847024458

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Advances in Hypercomplex Analysis by Graziano Gentili,Irene Sabadini,Michael Shapiro,Franciscus Sommen,Daniele C. Struppa Pdf

This volume is intended to collect important research results to the lectures and discussions which took Place in Rome, at the INdAM Workshop on Different Notions of Regularity for Functions of Quaternionic Variables in September 2010. This volume will collect recent and new results, which are connected to the topic covered during the workshop. The work aims at bringing together international leading specialists in the field of Quaternionic and Clifford Analysis, as well as young researchers interested in the subject, with the idea of presenting and discussing recent results, analyzing new trends and techniques in the area and, in general, of promoting scientific collaboration. Particular attention is paid to the presentation of different notions of regularity for functions of hypercomplex variables, and to the study of the main features of the theories that they originate.

Wavelets, Multiscale Systems and Hypercomplex Analysis

Daniel Alpay
Wavelets Multiscale Systems and Hypercomplex Analysis Book PDF

Author : Daniel Alpay
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 43,7 Mb
Release : 2006-08-06
Category : Mathematics
ISBN : 9783764375881

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Wavelets, Multiscale Systems and Hypercomplex Analysis by Daniel Alpay Pdf

This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications. Most of the articles have been written on invitation and they provide a unique collection of material, particularly relating to Clifford analysis and the theory of wavelets.

Operator Theory for Complex and Hypercomplex Analysis

Enrique Ramírez de Arellano,N. Salinas,M. V. Shapiro,N. L. Vasilevski
Operator Theory for Complex and Hypercomplex Analysis Book PDF

Author : Enrique Ramírez de Arellano,N. Salinas,M. V. Shapiro,N. L. Vasilevski
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 49,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806777

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Operator Theory for Complex and Hypercomplex Analysis by Enrique Ramírez de Arellano,N. Salinas,M. V. Shapiro,N. L. Vasilevski Pdf

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 operators, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure operator 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 for Complex and Hypercomplex Analysis'', held in December 1994 in Mexico City.

Linear Systems, Signal Processing and Hypercomplex Analysis

Daniel Alpay,Mihaela B. Vajiac
Linear Systems Signal Processing and Hypercomplex Analysis Book PDF

Author : Daniel Alpay,Mihaela B. Vajiac
Publisher : Springer
Page : 316 pages
File Size : 48,8 Mb
Release : 2019-08-08
Category : Mathematics
ISBN : 9783030184841

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Linear Systems, Signal Processing and Hypercomplex Analysis by Daniel Alpay,Mihaela B. Vajiac Pdf

This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.

Harmonic Analysis in Hypercomplex Systems

Yu.M. Berezansky,A.A. Kalyuzhnyi
Harmonic Analysis in Hypercomplex Systems Book PDF

Author : Yu.M. Berezansky,A.A. Kalyuzhnyi
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 42,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401717588

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Harmonic Analysis in Hypercomplex Systems by Yu.M. Berezansky,A.A. Kalyuzhnyi Pdf

First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative

Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac
New Directions in Function Theory From Complex to Hypercomplex to Non Commutative Book PDF

Author : Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac
Publisher : Springer Nature
Page : 389 pages
File Size : 52,9 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030764739

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New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative by Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac Pdf

This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.

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 : 52,7 Mb
Release : 2001-07-31
Category : Mathematics
ISBN : 0792370449

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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.

Computational Science and Its Applications - ICCSA 2011

Beniamino Murgante,Osvaldo Gervasi,Andres Iglesias,David Taniar,Bernady O. Apduhan
Computational Science and Its Applications ICCSA 2011 Book PDF

Author : Beniamino Murgante,Osvaldo Gervasi,Andres Iglesias,David Taniar,Bernady O. Apduhan
Publisher : Springer
Page : 700 pages
File Size : 47,7 Mb
Release : 2011-06-17
Category : Computers
ISBN : 9783642219313

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Computational Science and Its Applications - ICCSA 2011 by Beniamino Murgante,Osvaldo Gervasi,Andres Iglesias,David Taniar,Bernady O. Apduhan Pdf

The five-volume set LNCS 6782 - 6786 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2011, held in Santander, Spain, in June 2011. The five volumes contain papers presenting a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The topics of the fully refereed papers are structured according to the five major conference themes: geographical analysis, urban modeling, spatial statistics; cities, technologies and planning; computational geometry and applications; computer aided modeling, simulation, and analysis; and mobile communications.

Application of Holomorphic Functions in Two and Higher Dimensions

Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Application of Holomorphic Functions in Two and Higher Dimensions Book PDF

Author : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Publisher : Springer
Page : 390 pages
File Size : 55,5 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783034809641

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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig Pdf

This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.

Regular Functions of a Quaternionic Variable

Graziano Gentili,Caterina Stoppato,Daniele C. Struppa
Regular Functions of a Quaternionic Variable Book PDF

Author : Graziano Gentili,Caterina Stoppato,Daniele C. Struppa
Publisher : Springer Nature
Page : 302 pages
File Size : 54,7 Mb
Release : 2022-09-23
Category : Mathematics
ISBN : 9783031075315

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Regular Functions of a Quaternionic Variable by Graziano Gentili,Caterina Stoppato,Daniele C. Struppa Pdf

This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications. As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four. This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.

Noncommutative Functional Calculus

Prof. Fabrizio Colombo Politecnico di Milano,Irene Sabadini,Daniele C. Struppa
Noncommutative Functional Calculus Book PDF

Author : Prof. Fabrizio Colombo Politecnico di Milano,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 54,5 Mb
Release : 2011-03-18
Category : Mathematics
ISBN : 9783034801102

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Noncommutative Functional Calculus by Prof. Fabrizio Colombo Politecnico di Milano,Irene Sabadini,Daniele C. Struppa Pdf

This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.