International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 247-256

Function theory for a beltrami algebra

B. A. Case

Department of Mathematics, The Florida State University, Tallahassee 32306, Florida, USA

Received 16 July 1984

Copyright © 1985 B. A. Case. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.