Regular Functions of a Quaternionic Variable: Springer Monographs in Mathematics
Autor Graziano Gentili, Caterina Stoppato, Daniele C. Struppaen Limba Engleză Paperback – 26 sep 2023
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.
Toate formatele și edițiile | Preț | Express |
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Paperback (1) | 559.99 lei 38-44 zile | |
Springer International Publishing – 26 sep 2023 | 559.99 lei 38-44 zile | |
Hardback (1) | 575.49 lei 38-44 zile | |
Springer International Publishing – 25 sep 2022 | 575.49 lei 38-44 zile |
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Specificații
ISBN-13: 9783031075339
ISBN-10: 3031075331
Pagini: 285
Ilustrații: XXV, 285 p. 9 illus., 7 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:2nd ed. 2022
Editura: Springer International Publishing
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3031075331
Pagini: 285
Ilustrații: XXV, 285 p. 9 illus., 7 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:2nd ed. 2022
Editura: Springer International Publishing
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:Cham, Switzerland
Cuprins
Introduction.- 1.Definitions and Basic Results.- 2.Regular Power Series.- 3.Zeros.- 4.Infinite Products.- 5.Singularities.- 6.Integral Representations.- 7.Maximum Modulus Theorem and Applications.- 8.Spherical Series and Differential.- 9.Fractional Transformations and the Unit Ball.- 10.Generalizations.- 11. Function Theory over Non-symmetric Slice Domains.-12. Applications.- Bibliography.- Index.
Textul de pe ultima copertă
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.
“[The authors] 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)"
Caracteristici
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