Overview
- The book is entirely devoted to a new theory
- Presents a state of the art survey of the theory of slice regular functions ?
- The theory presented in the book is the basis for the solution to an outstanding problem, the construction of functional calculus in non commutative settings
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research community. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one complex variable and its wide variety of applications are a strong motivation for the study of its analogs in higher dimensions. In this respect, the four-dimensional case is particularly interesting due to its relevance in physics and its algebraic properties, as the quaternion forms the only associative real division algebra with a finite dimension n>2. Among other interesting function theories introduced in the quaternionic setting, that of (slice) regular functions shows particularly appealing features. For instance, this class of functions naturally includes polynomials and power series. The zero set of a slice regular function has an interesting structure, strictly linked to a multiplicative operation, and it allows the study of singularities. Integral representation formulas enrich the theory and they are a fundamental tool for one of the applications, the construction of a noncommutative functional calculus.
The volume presents a state-of-the-art survey of the theory and a brief overview of its generalizations and applications. It is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.
Reviews
From the reviews:
“Gentili (Univ. of Florence, Italy), Stoppato (Univ. of Milan, Italy), and Struppa (Chapman Univ.) document their own very recent theory of quaternionic regular functions, a development that parallels familiar complex function theory spectacularly well. This user-friendly primary source confirms that quaternionic calculus is not a dead end, and clearly answers a popular question regarding the analogy of complex function theory (complex analysis) with quarternionic variables, making it an excellent basis for a capstone course. Summing Up: Highly recommended. Upper-division undergraduates through professionals.” (D. V. Feldman, Choice, Vol. 51 (1), September, 2013)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/10.1007/978-3-642-33871-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
eBook ISBN: 978-3-642-33871-7Published: 11 January 2013
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIX, 185
Topics: Functions of a Complex Variable, Sequences, Series, Summability, Functional Analysis