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Weighted Uniform Convergence of Entire Grünwald Operators on the Real Line

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Abstract

We consider weighted uniform convergence of entire analogues of the Grünwald operator on the real line. The main result deals with convergence of entire interpolations of exponential type \(\tau >0\) at zeros of Bessel functions in spaces with homogeneous weights. We discuss extensions to Grünwald operators from de Branges spaces.

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Authors and Affiliations

  1. Department of Mathematics, North Dakota State University, Fargo, ND, 58108-6050, USA

    Friedrich Littmann

  2. The Beacom College of Computer and Cyber Sciences, Dakota State University, Madison, SD, 57042, USA

    Mark Spanier

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  1. Friedrich Littmann
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  2. Mark Spanier
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Correspondence to Friedrich Littmann.

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Communicated by Doron Lubinsky.

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Littmann, F., Spanier, M. Weighted Uniform Convergence of Entire Grünwald Operators on the Real Line. Comput. Methods Funct. Theory 22, 645–661 (2022). https://doi.org/10.1007/s40315-021-00408-2

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  • DOI: https://doi.org/10.1007/s40315-021-00408-2

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