International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 247-256
doi:10.1155/S0161171285000278

Function theory for a Beltrami algebra

Abstract

Complex functions are investigated which are solutions of an elliptic system of partial differential equations associated with a real parameter function. The functions f associated with a particualr parameter function g on a domain D form a Beltrami algebra denoted by the pair (D,g) and a function theory is developed in this algebra. A strong conformality property holds for all functions in a (D,g) algebra. For g≡|z|=r the algebra (D,r) is that of the analytic functions.