Hypercomplex Analysis And Applications
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Author | : Irene Sabadini |
Publisher | : Springer Science & Business Media |
Total Pages | : 280 |
Release | : 2010-12-20 |
Genre | : Mathematics |
ISBN | : 3034602464 |
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 | : Swanhild Bernstein |
Publisher | : Springer |
Total Pages | : 228 |
Release | : 2014-10-10 |
Genre | : Mathematics |
ISBN | : 3319087711 |
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 | : I.L. Kantor |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2011-09-21 |
Genre | : Mathematics |
ISBN | : 9781461281917 |
This book deals with various systems of "numbers" that can be constructed by adding "imaginary units" to the real numbers. The complex numbers are a classical example of such a system. One of the most important properties of the complex numbers is given by the identity (1) Izz'l = Izl·Iz'I· It says, roughly, that the absolute value of a product is equal to the product of the absolute values of the factors. If we put z = al + a2i, z' = b+ bi, 1 2 then we can rewrite (1) as The last identity states that "the product of a sum of two squares by a sum of two squares is a sum of two squares. " It is natural to ask if there are similar identities with more than two squares, and how all of them can be described. Already Euler had given an example of an identity with four squares. Later an identity with eight squares was found. But a complete solution of the problem was obtained only at the end of the 19th century. It is substantially true that every identity with n squares is linked to formula (1), except that z and z' no longer denote complex numbers but more general "numbers" where i,j, . . . , I are imaginary units. One of the main themes of this book is the establishing of the connection between identities with n squares and formula (1).
Author | : Graziano Gentili |
Publisher | : Springer Science & Business Media |
Total Pages | : 149 |
Release | : 2012-11-14 |
Genre | : Mathematics |
ISBN | : 8847024455 |
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.
Author | : Rafał Abłamowicz |
Publisher | : Springer Science & Business Media |
Total Pages | : 500 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780817641825 |
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.
Author | : Irene Sabadini |
Publisher | : Springer Science & Business Media |
Total Pages | : 289 |
Release | : 2009-04-21 |
Genre | : Mathematics |
ISBN | : 3764398930 |
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 | : Swanhild Bernstein |
Publisher | : Birkhäuser |
Total Pages | : 310 |
Release | : 2016-11-21 |
Genre | : Mathematics |
ISBN | : 3319425293 |
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.
Author | : Prof. Fabrizio Colombo Politecnico di Milano |
Publisher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2011-03-18 |
Genre | : Mathematics |
ISBN | : 3034801106 |
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.
Author | : Yumei Dang |
Publisher | : World Scientific |
Total Pages | : 163 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9810232969 |
Includes an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry.
Author | : Enrique Ramírez de Arellano |
Publisher | : American Mathematical Soc. |
Total Pages | : 312 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821806777 |
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.