Holomorphic Functions in the Plane and N-Dimensional Space

Gurlebeck K., Sprobig W.

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.

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Table of contents :
Preface to the German Edition……Page 9
Preface to the English Edition……Page 12
Contents……Page 4
Numbers……Page 13
Functions……Page 85
Integration and integral theorems……Page 137
Series expansions and local behavior……Page 173
Appendix……Page 335
A.1 Differential forms in Rn……Page 336
A.2 Integration and manifolds……Page 350
A.3 Some function spaces……Page 369
A.4 Properties of holomorphic spherical functions……Page 375
Bibliography……Page 389
Index……Page 397