Interpolation formulas with derivatives in de Branges spaces

Gonçalves, Felipe

doi:10.1090/tran6672

Interpolation formulas with derivatives in de Branges spaces
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Trans. Amer. Math. Soc. 369 (2017), 805-832 Request permission

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 1985 to general $L^p$ de Branges spaces. We extensively use techniques from de Branges’ theory of Hilbert spaces of entire functions, but a crucial passage involves the Hilbert-type inequalities as derived by Carneiro, Littmann, and Vaaler. 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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