Semigroups and generators on convex domains with the hyperbolic metric
type: Item
instance of: scholarly article
title: Semigroups and generators on convex domains with the hyperbolic metric
zbMATH Open document ID: 0905.47056
author: Simeon Reich
author: David Shoikhet
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1999-02-03T00:00:00Z
full work available at URL: https://eudml.org/doc/244272
review text: Summary: Let \(D\) be domain in a complex Banach space \(X\), and let \(\varrho\) be a pseudometric assigned to \(D\) by a Schwarz-Pick system. In the first section of the paper, we establish several criteria for a mapping \(f: D\to X\) to be a generator of a \(\varrho\)-nonexpansive semigroup on \(D\) in terms of its nonlinear resolvent. In the second section, we let \(X= H\) be a complex Hilbert space, \(D= B\) the open unit ball of \(H\), and \(\varrho\) the hyperbolic metric on \(B\). We introduce the notion of a \(\varrho\)-monotone mapping and obtain simple characterizations of generators of semigroups of holomorphic selfmappings of \(B\).
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 1210263
zbMATH Keywords: monotone operator
zbMATH Keywords: pseudometric
zbMATH Keywords: Schwarz-Pick system
zbMATH Keywords: generator of a \(\varrho\)-nonexpansive semigroup
zbMATH Keywords: nonlinear resolvent
zbMATH Keywords: hyperbolic metric
zbMATH Keywords: semigroups of holomorphic selfmappings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1210263