Holomorphic Functions in the Plane and n-dimensional Space

• Main Authors: Gürlebeck, Klaus (Author), Habetha, Klaus (Author), Sprößig, Wolfgang (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functions of complex variables.; Integral transforms.; Operational calculus.; Potential theory (Mathematics).; Functions of a Complex Variable.; Integral Transforms, Operational Calculus.; Potential Theory.; Analysis.
• Physical Description: XIV, 394 p. online resource.
• ISBN: 9783764382728

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.