Holomorphic Functions in the Plane and N-Dimensional Space

by Gurlebeck, Klaus; Habetha, Klaus; Sprossig, Wolfgang

• ISBN13: 9783764382711
• ISBN10: 3764382716
• Edition: CD
• Format: Paperback
• Copyright: 2008-01-03
• Publisher: Birkhauser

Summary

Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or 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.

Table of Contents

Numbers	p. 1
Complex numbers	p. 2
Quaternions	p. 15
Clifford numbers	p. 50
Functions	p. 73
Topological aspects	p. 74
Holomorphic functions	p. 90
Powers and Mobius transforms	p. 108
Integration and integral theorems	p. 125
Integral theorems and integral formulae	p. 126
Teodorescu transform	p. 151
Series expansions and local behavior	p. 161
Power series	p. 162
Orthogonal expansions in H	p. 186
Elementary functions	p. 218
Local structure of holomorphic functions	p. 252
Special functions	p. 287
Appendix	p. 323
Bibliography	p. 377
Index	p. 385
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