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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Regular Functions of a Quaternionic Variable
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Regular Functions of a Quaternionic Variable
Graziano Gentili, Caterina Stoppato, Daniele C. Struppa (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.09.2023
Sprache
Englisch
EAN
9783031075339
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Graziano Gentili, Caterina Stoppato, Daniele C. Struppa
Seitenanzahl
285
Auflage
2
Einbandart
Broschiert
Schlagwörter
30G35, 30B10, 30C15, 30E20, 30C80, Functions of one quaterionic variable, Quaterionic power series, Maximum and Minimum Modulus Principle, Zero sets, Singularities, Integral representations, Open Mapping Theorem, Function theory over the quterionic unit ball
Thema-Inhalt
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PBK - Mathematische Analysis, allgemein
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Palgrave Macmillan, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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