Spherical $\Pi$-type Operators in Clifford Analysis and Applications
Complex Variables
2016-09-12 v1
Abstract
The -operator (Ahlfors-Beurling transform) plays an important role in solving the Beltrami equation. In this paper we define two -operators on the n-sphere. The first spherical -operator is shown to be an isometry up to isomorphism. To improve this, with the help of the spectrum of the spherical Dirac operator, the second spherical operator is constructed as an isometric operator over the sphere. Some analogous properties for both -operators are also developed. We also study the applications of both spherical -operators to the solution of the spherical Beltrami equations.
Cite
@article{arxiv.1609.02840,
title = {Spherical $\Pi$-type Operators in Clifford Analysis and Applications},
author = {Wanqing Cheng and John Ryan and Uwe Kähler},
journal= {arXiv preprint arXiv:1609.02840},
year = {2016}
}