Multipliers for entire functions and an interpolation problem of Beurling
type: Item
instance of: scholarly article
title: Multipliers for entire functions and an interpolation problem of Beurling
zbMATH Open document ID: 0916.30036
author: Joaquim Ortega-Cerdà
author: Kristian Seip
published in: Journal of Functional Analysis
publication date: 1999-07-12T00:00:00Z
full work available at URL: http://hdl.handle.net/2445/164425
review text: Let \(B_\tau\) be the set of all entire functions of exponential type at most \(\tau\) whose restriction to the real line belong to \(L^\infty(R)\) and let \(\Lambda=\{\lambda_k\}\) be a sequence of distinct points in \(\mathbb{C}\) such that for any \(\{a_k\}\), \(\sup_k| a_k| e^{-\tau|{\mathfrak F} \lambda_k|} <\infty\), the interpolation problem \(f(\lambda_k)=a_k\) has a solution \(f\in B_\tau\), i.e. \(\Lambda\) is an interpolating sequence for \(B_\tau\). The authors prove the criterion of the interpolating sequence for \(B_\tau\).
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 1274806
zbMATH Keywords: entire functions of exponential type
zbMATH Keywords: interpolation problem
zbMATH Keywords: interpolating sequence
reviewed by: P. Z. Agranovich
MaRDI profile type: Publication
OpenAlex ID: W2031067200
cites work: Q3331503
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DOI: 10.1006/JFAN.1998.3357
description: scientific article; zbMATH DE number 1274806