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

B. A. Case

 Department of Mathematics, The Florida State University, Tallahassee 32306, Florida, USA
Received 16 July 1984

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.