Regular Functions of a Quaternionic Variable is popular PDF and ePub book, written by Graziano Gentili in 2022-09-23, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Regular Functions of a Quaternionic Variable can be Read Online from any device for your convenience.
Regular Functions of a Quaternionic Variable Book PDF Summary
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.
Detail Book of Regular Functions of a Quaternionic Variable PDF
- Author : Graziano Gentili
- Release : 23 September 2022
- Publisher : Springer Nature
- ISBN : 9783031075315
- Genre : Mathematics
- Total Page : 302 pages
- Language : English
- PDF File Size : 20,9 Mb
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