Compactness of resolvent operators generated by a class of composition semigroups on \(H^ p\)
type: Item
instance of: scholarly article
title: Compactness of resolvent operators generated by a class of composition semigroups on \(H^ p\)
zbMATH Open document ID: 0715.47029
DOI: 10.1016/0022-247X(90)90391-R
author: Alexandru Aleman
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Let \(H^ p\) be the Hardy space for the unit disk D, \(1\leq p<\infty\). A composition semigroup on \(H^ p\) is given by \(T_ tf=f\circ \vartheta_ t\quad (f\in H^ p,\quad t\geq 0),\) where \(\{\vartheta_ t:\) \(t\geq 0\}\) is a semigroup (under conposition) of analytic functions from D to D. Such objects were studied by E. Berkson and H. Porta. The author extends work of \textit{A. G. Siskakis} [J. Math. Anal. Appl. 127, 122-129 (1987; Zbl 0645.47032)]. Of concern is the resolvent \(R(\lambda,A_ p)\) of the generator \(A_ p\) of \(\{T_ t\}\). Criteria (and related examples) are given for the compactness of \(R(\lambda,A_ p)\).
reviewed by: Jerome A. Goldstein
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4177947
zbMATH Keywords: Hardy space for the unit disk
zbMATH Keywords: composition semigroup on \(H^ p\)
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4177947