# Weighted Uniform Convergence of Entire Grünwald Operators on the Real Line

Weighted Uniform Convergence of Entire Grünwald Operators on the Real Line 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 τ>0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\tau >0$$\end{document} at zeros of Bessel functions in spaces with homogeneous weights. We discuss extensions to Grünwald operators from de Branges spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Weighted Uniform Convergence of Entire Grünwald Operators on the Real Line

, Volume 22 (4): 17 – Dec 1, 2022
17 pages

/lp/springer-journals/weighted-uniform-convergence-of-entire-gr-nwald-operators-on-the-real-mq35TfxQTX
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00408-2
Publisher site
See Article on Publisher Site

### 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 τ>0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\tau >0$$\end{document} at zeros of Bessel functions in spaces with homogeneous weights. We discuss extensions to Grünwald operators from de Branges spaces.

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Dec 1, 2022

Keywords: Grünwald operator; Hermite–Fejér interpolation; Weighted uniform approximation; de Branges space; Exponential type; 41A05; 41A17; 30E05

### References

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