Holomorphic Functions in the Plane and n-dimensional Space
Title:
Holomorphic Functions in the Plane and n-dimensional Space
Author:
Gürlebeck, Klaus. author.
ISBN:
9783764382728
Personal Author:
Physical Description:
XIV, 394 p. online resource.
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.
Abstract:
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.
Added Corporate Author:
Electronic Access:
http://dx.doi.org/10.1007/978-3-7643-8272-8