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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 (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
19.06.2015
Sprache
Englisch
EAN
9783642440540
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Graziano Gentili
Seitenanzahl
185
Einbandart
Broschiert
Schlagwörter
30G35, 30B10, 30C15, 30E20, 30C80, Schwarz's lemma, functions of hypercomplex variables and generalized variables, maximum principle, power series, zeros of polynomials
Thema-Inhalt
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PBK - Mathematische Analysis, allgemein
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
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