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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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


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:
  • Received by editor(s): October 20, 2014
  • Received by editor(s) in revised form: January 23, 2015
  • Published electronically: March 1, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 805-832
  • MSC (2010): Primary 46E22, 30D10, 41A05, 41A30, 33C10
  • DOI:
  • MathSciNet review: 3572255