On the differentiability ofT(r,f)

Douglas W. Townsed
1982 International Journal of Mathematics and Mathematical Sciences  
It is well known thatT(r,f)is differentiable at least forr>r0. We show that, in fact,T(r,f)is differentiable for all but at most one value ofr, and ifT(r,f)fails to have a derivative for some value ofr, thenfis a constant times a quotient of finite Blaschke products.
doi:10.1155/s0161171282000337 fatcat:xnutwwucwzcehl5jvh4q4fruia