Geodesic
Radial N-th Derivatives of Bounded Analytic Operator Functions
Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 111 .

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We give, roughly, necessary and sufficient conditions, in terms of the Potapov-Ginzburg factorization, for the existence of $N$-th radial derivatives of bounded analytic operator functions. Our result is a generalization of the result of Ahern and Clark concerning scalar functions [1]. For inner matrix functions (in the case $N$ odd) such a result was proved in [2].
Classification : 30G35 47B38
Keywords: analytic operator function, radial derivative, operator-valued kernel 
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     author = {Du\v{s}an Georgijevi\'c},
     title = {Radial {N-th} {Derivatives} of {Bounded} {Analytic} {Operator} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
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     year = {1991},
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Dušan Georgijević. Radial N-th Derivatives of Bounded Analytic Operator Functions. Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 111 . http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a13/