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Holomorphic Functions in the Plane and n-dimensional Space

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...

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Main Authors: Gürlebeck, Klaus. (Author, http://id.loc.gov/vocabulary/relators/aut), Habetha, Klaus. (http://id.loc.gov/vocabulary/relators/aut), Sprößig, Wolfgang. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2008.
Edition:1st ed. 2008.
Subjects:
Functions of complex variables.
Integral transforms.
Operational calculus.
Potential theory (Mathematics).
Mathematical analysis.
Analysis (Mathematics).
Functions of a Complex Variable.
Integral Transforms, Operational Calculus.
Potential Theory.
Analysis.
Online Access:https://doi.org/10.1007/978-3-7643-8272-8
Table of 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.

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