Hypercomplex Analysis: New Perspectives and Applications

Hypercomplex Analysis: New Perspectives and Applications
Title Hypercomplex Analysis: New Perspectives and Applications PDF eBook
Author Swanhild Bernstein
Publisher Springer
Pages 228
Release 2014-10-10
Genre Mathematics
ISBN 3319087711

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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

Modern Trends in Hypercomplex Analysis
Title Modern Trends in Hypercomplex Analysis PDF eBook
Author Swanhild Bernstein
Publisher Birkhäuser
Pages 310
Release 2016-11-21
Genre Mathematics
ISBN 3319425293

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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.

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

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative
Title New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative PDF eBook
Author Daniel Alpay
Publisher Springer Nature
Pages 389
Release 2022-01-01
Genre Mathematics
ISBN 3030764737

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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.

Entire Slice Regular Functions

Entire Slice Regular Functions
Title Entire Slice Regular Functions PDF eBook
Author Fabrizio Colombo
Publisher Springer
Pages 121
Release 2016-12-08
Genre Mathematics
ISBN 3319492659

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This Briefs volume develops the theory of entire slice regular functions. It is the first self-contained, monographic work on the subject, offering all the necessary background information and detailed studies on several central topics, including estimates on the minimum modulus of regular functions, relations between Taylor coefficients and the growth of entire functions, density of their zeros, and the universality properties. The proofs presented here shed new light on the nature of the quaternionic setting and provide inspiration for further research directions. Also featuring an exhaustive reference list, the book offers a valuable resource for graduate students, postgraduate students and researchers in various areas of mathematical analysis, in particular hypercomplex analysis and approximation theory.

Regular Functions of a Quaternionic Variable

Regular Functions of a Quaternionic Variable
Title Regular Functions of a Quaternionic Variable PDF eBook
Author Graziano Gentili
Publisher Springer Nature
Pages 302
Release 2022-09-23
Genre Mathematics
ISBN 3031075315

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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.

Computational Science and Its Applications - ICCSA 2014

Computational Science and Its Applications - ICCSA 2014
Title Computational Science and Its Applications - ICCSA 2014 PDF eBook
Author Beniamino Murgante
Publisher Springer
Pages 869
Release 2014-07-03
Genre Computers
ISBN 3319091441

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The six-volume set LNCS 8579-8584 constitutes the refereed proceedings of the 14th International Conference on Computational Science and Its Applications, ICCSA 2014, held in Guimarães, Portugal, in June/July 2014. The 347 revised papers presented in 30 workshops and a special track were carefully reviewed and selected from 1167 initial submissions. The 289 papers presented in the workshops cover various areas in computational science ranging from computational science technologies to specific areas of computational science such as computational geometry and security.

Noncommutative Analysis, Operator Theory and Applications

Noncommutative Analysis, Operator Theory and Applications
Title Noncommutative Analysis, Operator Theory and Applications PDF eBook
Author Daniel Alpay
Publisher Birkhäuser
Pages 285
Release 2016-06-30
Genre Mathematics
ISBN 3319291165

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This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.