Operators commuting with the multiple integration in the space of analytic functions
type: Item
instance of: scholarly article
title: Operators commuting with the multiple integration in the space of analytic functions
zbMATH Open document ID: 0606.47034
DOI: 10.1007/BF00969393
author: M. I. Nagnybida
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let D be a star-shaped (w.r.t. zero) domain in the complex plane. Let \((If)(z)=\int^{z}_{0}f(\zeta)d\zeta\) be the integration operator in the space A(D) of analytic functions on D. Let p be a positive integer. The author describes the commutant of \(I^ p\) in A(D). The results depend on the rotation properties of D. Similar results are obtained for the multiplication operator \((Uf)(z)=zf(z)\).
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 3979835
zbMATH Keywords: operator in the space of analytic functions
zbMATH Keywords: commutant
zbMATH Keywords: rotation
zbMATH Keywords: multiplication operator
reviewed by: Jaroslav Zemánek
MaRDI profile type: Publication
cites work: Q3660037
cites work: Conditions for triviality of a class of operators in an analytic space
cites work: Q3049387
cites work: Q3945042
cites work: Q3036134
full work available at URL: https://doi.org/10.1007/bf00969393
OpenAlex ID: W1998535035
description: scientific article; zbMATH DE number 3979835