On the nonexistence of a continuous linear operator of a certain form from S to H(D)
type: Item
instance of: scholarly article
title: On the nonexistence of a continuous linear operator of a certain form from S to H(D)
zbMATH Open document ID: 0727.46010
DOI: 10.1007/BF01198924
author: Leonid Brevdo
published in: Integral Equations and Operator Theory
publication date: 1990-01-01T00:00:00Z
review text: Let D be a domain in the complex plane and \(\{a_ k\}\subset D\)- a fixed sequence of distinct points with no points of accumulation in D. Let S be the space of all sequences with coordinate convergence and H(D) be the space of all holomorphic functions on D with topology of uniform convergence on compact subsets. Theorem. There does not exist a continuous operator A from S into H(D) such that \(A(\{b_ k\})=f_ b(z)\), where \(f_ b(a_ k)=b_ k\) (k\(\geq 1).\) This result can be related to interpolation in spaces of holomorphic functions.
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 4200921
zbMATH Keywords: interpolation in spaces of holomorphic functions
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
cites work: An Interpolation Problem for Bounded Analytic Functions
cites work: Q4402191
cites work: Q5727906
cites work: On Some Interpolation Problems for Analytic Functions
full work available at URL: https://doi.org/10.1007/bf01198924
OpenAlex ID: W2089587370
description: scientific article; zbMATH DE number 4200921