Gürlebeck / Habetha / Sprößig Holomorphic Functions in the Plane and n-dimensional Space

Erscheinungsjahr 2007
ISBN: 978-3-7643-8272-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 394 Seiten, eBook

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.

Zielgruppe

Research

Autoren/Hrsg.

Gürlebeck, Klaus

Habetha, Klaus

Sprößig, Wolfgang

Inhaltsverzeichnis

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.