Overview
- Entirely devoted to the theory of slice regular functions
- Surveys the foundations of the theory and gives an overview of its applications
- Covers the newly developed function theory over domains that are not axially symmetric
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Regular Functions of a Quaternionic Variable
Authors: Graziano Gentili, Caterina Stoppato, Daniele C. Struppa
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-031-07531-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-07530-8Published: 25 September 2022
Softcover ISBN: 978-3-031-07533-9Published: 26 September 2023
eBook ISBN: 978-3-031-07531-5Published: 23 September 2022
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 2
Number of Pages: XXV, 285
Number of Illustrations: 2 b/w illustrations, 7 illustrations in colour
Topics: Functions of a Complex Variable, Sequences, Series, Summability, Functional Analysis