Integral representation{Integral representation of the $n$-th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernelReport as inadecuate




Integral representation{Integral representation of the $n$-th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel - Download this document for free, or read online. Document in PDF available to download.

1 ICJ - Institut Camille Jordan Villeurbanne 2 Université LAVAL, Département de Mathématiques et de Statistiques

Abstract : In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges-Rovnyak spaces $\HHb$, where $b$ is in the unit ball of $H^\infty\CC +$. 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 $k {\omega,n}^b$ of the evaluation of $n$-th derivative of elements of $\HHb$ at the point $\omega$ as it tends radially to a point of the real axis.





Author: Emmanuel Fricain - Javad Mashreghi -

Source: https://hal.archives-ouvertes.fr/



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