Analysis Of Dirac Systems And Computational Algebra

Author : Fabrizio Colombo,Irene Sabadini,Franciscus Sommen,Daniele C. Struppa
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681661

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Analysis of Dirac Systems and Computational Algebra by Fabrizio Colombo,Irene Sabadini,Franciscus Sommen,Daniele C. Struppa Pdf

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

Author : F. Colombo,I. Sabadini
Publisher : Unknown
Page : 128 pages
File Size : 45,9 Mb
Release : 2004
Category : Electronic
ISBN : 3764342552

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Analysis of Dirac Systems and Computational Algebra by F. Colombo,I. Sabadini Pdf

Author : Daniel Alpay,Victor Vinnikov
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 50,7 Mb
Release : 2007-03-20
Category : Mathematics
ISBN : 9783764381363

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System Theory, the Schur Algorithm and Multidimensional Analysis by Daniel Alpay,Victor Vinnikov Pdf

This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Author : Lawrence Zalcman
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 46,7 Mb
Release : 2016-05-19
Category : Calculus of variations
ISBN : 9781470417031

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Complex Analysis and Dynamical Systems VI by Lawrence Zalcman Pdf

This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.

Author : Irene Sabadini,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 48,5 Mb
Release : 2010-12-20
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.

Author : Irene Sabadini,Michael Shapiro,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 49,5 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.

Author : John Ryan,Daniele C Struppa
Publisher : CRC Press
Page : 260 pages
File Size : 55,9 Mb
Release : 1999-01-06
Category : Mathematics
ISBN : 0582356814

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Dirac Operators in Analysis by John Ryan,Daniele C Struppa Pdf

Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.

Author : Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Nature
Page : 126 pages
File Size : 49,5 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030502164

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Michele Sce's Works in Hypercomplex Analysis by Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Pdf

This book presents English translations of Michele Sce’s most important works, originally written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of hypercomplex numbers. Despite their importance, these works are not very well known in the mathematics community because of the language they were published in. Possibly the most remarkable instance is the so-called Fueter-Sce mapping theorem, which is a cornerstone of modern hypercomplex analysis, and is not yet understood in its full generality. This volume is dedicated to revealing and describing the framework Sce worked in, at an exciting time when the various generalizations of complex analysis in one variable were still in their infancy. In addition to faithfully translating Sce’s papers, the authors discuss their significance and explain their connections to contemporary research in hypercomplex analysis. They also discuss many concrete examples that can serve as a basis for further research. The vast majority of the results presented here will be new to readers, allowing them to finally access the original sources with the benefit of comments from fellow mathematicians active in the field of hypercomplex analysis. As such, the book offers not only an important chapter in the history of hypercomplex analysis, but also a roadmap for further exciting research in the field.

Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen
Publisher : Springer
Page : 228 pages
File Size : 52,8 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.

Author : R. Delanghe,F. Sommen,V. Soucek
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401129220

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Clifford Algebra and Spinor-Valued Functions by R. Delanghe,F. Sommen,V. Soucek Pdf

This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some Appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.

Author : Swanhild Bernstein
Publisher : Springer Nature
Page : 503 pages
File Size : 40,6 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9783030238544

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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.

Author : Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Nature
Page : 424 pages
File Size : 41,9 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9783031214608

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Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis by Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Pdf

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

Author : Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa,Mihaela B. Vajiac
Publisher : Birkhäuser
Page : 398 pages
File Size : 52,5 Mb
Release : 2017-09-30
Category : Mathematics
ISBN : 9783319623627

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Advances in Complex Analysis and Operator Theory by Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa,Mihaela B. Vajiac Pdf

This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

Author : Graziano Gentili,Caterina Stoppato,Daniele C. Struppa
Publisher : Springer Nature
Page : 302 pages
File Size : 49,7 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.

Author : Salvatore COEN
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 47,6 Mb
Release : 2012-05-11
Category : Mathematics
ISBN : 9783034802277

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Mathematicians in Bologna 1861–1960 by Salvatore COEN Pdf

The scientific personalities of Luigi Cremona, Eugenio Beltrami, Salvatore Pincherle, Federigo Enriques, Beppo Levi, Giuseppe Vitali, Beniamino Segre and of several other mathematicians who worked in Bologna in the century 1861–1960 are examined by different authors, in some cases providing different view points. Most contributions in the volume are historical; they are reproductions of original documents or studies on an original work and its impact on later research. The achievements of other mathematicians are investigated for their present-day importance.