Displaying similar documents to “Partial sums of certain analytic and univalent functions.”

Integral representation of the n -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel

Emmanuel Fricain, Javad Mashreghi (2008)

Annales de l’institut Fourier

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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 ∞ ( 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...