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Transactions of the American Mathematical Society

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Interpolation formulas with derivatives in de Branges spaces


Author: Felipe Gonçalves
Journal: Trans. Amer. Math. Soc. 369 (2017), 805-832
MSC (2010): Primary 46E22, 30D10, 41A05, 41A30, 33C10
DOI: https://doi.org/10.1090/tran6672
Published electronically: March 1, 2016
MathSciNet review: 3572255
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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 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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Additional Information

Felipe Gonçalves
Affiliation: IMPA - Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, Rio de Janeiro, RJ, Brazil 22460-320
Email: ffgoncalves@impa.br

DOI: https://doi.org/10.1090/tran6672
Keywords: De Branges spaces, Hilbert spaces of entire functions, exponential type, interpolation formulas, Bessel functions, homogeneous spaces, extremal functions
Received by editor(s): October 20, 2014
Received by editor(s) in revised form: January 23, 2015
Published electronically: March 1, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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