A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this paper the authors study the corresponding situation for solutions to Stein-Weiss systems in the nD Euclidean space. We add a more precise meaning by pointing out that a generalized holomorphic function asymptotically maps the unit sphere onto explicitly characterized ellipsoids and vice versa. Ultimately, we illustrate our approach using a typical example.
Local distortion of monogenic functions
9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012 ; 2012 ; Vienna, Austria
AIP Conference Proceedings ; 1493 , 1 ; 703-709
2012-11-06
7 pages
Conference paper
Electronic Resource
English
Local distortion of monogenic functions
British Library Conference Proceedings | 2012
|On pseudo-complex bases for monogenic polynomials
American Institute of Physics | 2012
|On pseudo-complex bases for monogenic polynomials
British Library Conference Proceedings | 2012
|Modular equations and distortion functions
British Library Online Contents | 2009
|The Monogenic Scale Space on a Rectangular Domain and its Features
British Library Online Contents | 2005
|