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Holomorphic Functions in the Plane and n-dimensional Space [electronic resource] /by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig.

by Gürlebeck, Klaus [author.]; Habetha, Klaus [author.]; Sprößig, Wolfgang [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Basel : Birkhäuser Basel, 2008.Description: XIV, 394 p. online resource.ISBN: 9783764382728.Subject(s): Mathematics | Global analysis (Mathematics) | Functions of complex variables | Integral Transforms | Potential theory (Mathematics) | Mathematics | Functions of a Complex Variable | Integral Transforms, Operational Calculus | Potential Theory | AnalysisDDC classification: 515.9 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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