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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Bicomplex Holomorphic Functions
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Bicomplex Holomorphic Functions
M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac (Broschiert, Englisch)
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Beschreibung
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers. Around the middle of the… nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something thatfor a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable. While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a “complexification” of the field of complex numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one-or multidimensional complex analysis. 58,84 €
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Technische Daten
Erscheinungsdatum
18.12.2015
Sprache
Englisch
EAN
9783319248660
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Frontiers in Mathematics
Sonderedition
Nein
Autor
M. Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa, Adrian Vajiac
Seitenanzahl
231
Einbandart
Broschiert
Buch Untertitel
The Algebra, Geometry and Analysis of Bicomplex Numbers
Schlagwörter
bicomplex elementary functions, bicomplex holomorphy, bicomplex numbers, complex holomorphic functions of 2 complex variables, geometry in 4‐dimensional space, hyperbolic numbers, hyperbolic-valued norm
Thema-Inhalt
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PHU - Mathematische Physik
Höhe
240 mm
Breite
16.8 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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