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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