Interpolation Formulas With Derivatives in De Branges Spaces

Felipe Gonçalves

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arXiv · 1503.05178

Interpolation Formulas With Derivatives in De Branges Spaces

Felipe Gonçalves

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Abstract

The purpose of this paper is to prove an interpolation formula involving derivatives for entire functions of exponential type. We extend the interpolation formula derived by J. Vaaler in [37, Theorem 9] to general $L^p$ de Branges spaces. We extensively use techniques from de Branges' theory of Hilbert spaces of entire functions as developed in [6], but a crucial passage involves the Hilbert-type inequalities as derived in [15]. We give applications to homogeneous spaces of entire functions that involve Bessel functions and we prove a uniqueness result for extremal one-sided band-limited approximations of radial functions in Euclidean spaces.

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Felipe Gonçalves. 2015-03-17. Interpolation Formulas With Derivatives in De Branges Spaces. https://arxiv.org/abs/1503.05178

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