International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 351-356

On the differentiability of T(r,f)

Douglas W. Townsed

Department of Mathematical Sciences, Indiana University-Purdue University at Fort Wayne, Fort Wayne 46805, Indiana, USA

Received 16 June 1980

Copyright © 1982 Douglas W. Townsed. 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.


It is well known that T(r,f) is differentiable at least for r>r0. We show that, in fact, T(r,f) is differentiable for all but at most one value of r, and if T(r,f) fails to have a derivative for some value of r, then f is a constant times a quotient of finite Blaschke products.