Partial sums of certain analytic and univalent functions.

Frasin, B.A.

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In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces $ℋ (b)$ , where $b$ is in the unit ball of $H^{\infty} (ℂ_{+})$ . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces $K_{b}$ , where $b$ is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel...

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