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.

Hypercomplex Analysis

Hypercomplex Analysis
Title Hypercomplex Analysis PDF eBook
Author Swanhild Bernstein
Publisher
Pages 236
Release 2014-10-31
Genre
ISBN 9783319087726

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Spectral Theory on the S-Spectrum for Quaternionic Operators

Spectral Theory on the S-Spectrum for Quaternionic Operators
Title Spectral Theory on the S-Spectrum for Quaternionic Operators PDF eBook
Author Fabrizio Colombo
Publisher Springer
Pages 357
Release 2019-01-04
Genre Mathematics
ISBN 3030030741

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The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.

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.

Hypercomplex Analysis and Applications

Hypercomplex Analysis and Applications
Title Hypercomplex Analysis and Applications PDF eBook
Author Irene Sabadini
Publisher Springer Science & Business Media
Pages 280
Release 2010-12-20
Genre Mathematics
ISBN 3034602464

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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.

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.

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.