Holomorphic Functions in the Plane and n-dimensional Space
by
Gürlebeck, Klaus. author.
Title
:
Holomorphic Functions in the Plane and n-dimensional Space
Author
:
Gürlebeck, Klaus. author.
ISBN
:
9783764382728
Personal Author
:
Gürlebeck, Klaus. 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.
Subject Term
:
Mathematics.
Global analysis (Mathematics).
Functions of complex variables.
Integral Transforms.
Potential theory (Mathematics).
Functions of a Complex Variable.
Integral Transforms, Operational Calculus.
Potential Theory.
Analysis.
Added Author
:
Habetha, Klaus.
Sprößig, Wolfgang.
Added Corporate Author
:
SpringerLink (Online service)
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | E-Book | 503884-1001 | QA331 -355 | Online Springer |