Weighted uniform convergence of entire Gr\"unwald operators on the real line

TL;DR

This paper investigates the weighted uniform convergence of entire Gr"unwald operators on the real line, focusing on their interpolation properties at Bessel function zeros and extensions to de Branges spaces.

Contribution

It introduces new convergence results for entire Gr"unwald operators with weighted uniform norms and extends the analysis to de Branges spaces.

Findings

Convergence of entire interpolations at Bessel zeros established.

Extensions of Gr"unwald operators to de Branges spaces discussed.

Results contribute to approximation theory in weighted function spaces.

Abstract

We consider weighted uniform convergence of entire analogues of the Gr\"unwald 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 Gr\"unwald operators from de Branges spaces.