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＜E-Book＞
Holomorphic Functions in the Plane and n-dimensional Space / by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig

Edition	1st ed. 2008.
Publisher	Basel : Birkhäuser Basel : Imprint: Birkhäuser
Year	2008
Language	English
Size	XIV, 394 p : online resource
Authors	*Gürlebeck, Klaus author Habetha, Klaus author Sprößig, Wolfgang author SpringerLink (Online service)
Subjects	LCSH:Functions of complex variables LCSH:Mathematical analysis LCSH:Potential theory (Mathematics) FREE:Functions of a Complex Variable FREE:Integral Transforms and Operational Calculus FREE:Potential Theory FREE:Analysis
Notes	Introduction -- I. Numbers -- Complex Numbers - Quaternions - Clifford numbers -- II. Functions -- Topological Aspects - Holomorphic Functions - Power Functions and Möbius Transformations -- III. Integration und Integral Theorems - Integral Theorems and -formulas - Teodorescu Transformation -- IV. Series and Local Properties - Power Series- Orthogonal Series - Elementary Functions -- Local Structure of Holomorphic Functions - Special Functions -- Appendices -- Bibliography -- Index Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter HTTP:URL=https://doi.org/10.1007/978-3-7643-8272-8

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