Semigroups and generators on convex domains with the hyperbolic metric

Simeon Reich; David Shoikhet

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 4, page 231-250
  • ISSN: 1120-6330

Abstract

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Let D be domain in a complex Banach space X , and let ρ 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 → X to be a generator of a ρ -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 ρ the hyperbolic metric on B . We introduce the notion of a ρ -monotone mapping and obtain simple characterizations of generators of semigroups of holomorphic self-mappings of B .

How to cite

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Reich, Simeon, and Shoikhet, David. "Semigroups and generators on convex domains with the hyperbolic metric." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.4 (1997): 231-250. <http://eudml.org/doc/244272>.

@article{Reich1997,
abstract = {Let \( D \) be domain in a complex Banach space \( X \), and let \( \rho \) 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 \( f : D \rightarrow X \) to be a generator of a \( \rho \)-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 \( \rho \) the hyperbolic metric on \( B \). We introduce the notion of a \( \rho \)-monotone mapping and obtain simple characterizations of generators of semigroups of holomorphic self-mappings of \( B \).},
author = {Reich, Simeon, Shoikhet, David},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Banach space; Generator; Holomorphic mapping; Hyperbolic metric; Monotone operator; monotone operator; pseudometric; Schwarz-Pick system; generator of a -nonexpansive semigroup; nonlinear resolvent; hyperbolic metric; semigroups of holomorphic selfmappings},
language = {eng},
month = {12},
number = {4},
pages = {231-250},
publisher = {Accademia Nazionale dei Lincei},
title = {Semigroups and generators on convex domains with the hyperbolic metric},
url = {http://eudml.org/doc/244272},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Reich, Simeon
AU - Shoikhet, David
TI - Semigroups and generators on convex domains with the hyperbolic metric
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/12//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 4
SP - 231
EP - 250
AB - Let \( D \) be domain in a complex Banach space \( X \), and let \( \rho \) 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 \( f : D \rightarrow X \) to be a generator of a \( \rho \)-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 \( \rho \) the hyperbolic metric on \( B \). We introduce the notion of a \( \rho \)-monotone mapping and obtain simple characterizations of generators of semigroups of holomorphic self-mappings of \( B \).
LA - eng
KW - Banach space; Generator; Holomorphic mapping; Hyperbolic metric; Monotone operator; monotone operator; pseudometric; Schwarz-Pick system; generator of a -nonexpansive semigroup; nonlinear resolvent; hyperbolic metric; semigroups of holomorphic selfmappings
UR - http://eudml.org/doc/244272
ER -

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