Comparison of semigroups and resolvents of order \(\alpha\) associated with differential operators of divergence type
type: Item
instance of: scholarly article
title: Comparison of semigroups and resolvents of order \(\alpha\) associated with differential operators of divergence type
zbMATH Open document ID: 0795.31008
DOI: 10.1007/BF01047834
author: Mohamed Selmi
published in: Potential Analysis
publication date: 1994-06-07T00:00:00Z
review text: \(L\) étant un opérateur différentiel du deuxième ordre, de type divergence, uniformément elliptique sur \(\mathbb{R}^ n\), on montre que la fonction de Green de l'opérateur \((-L)^ \alpha\) \((0< \alpha< 1)\), obtenu par subordination au sens de Bochner, est comparable au noyau de Riesz d'ordre \(\alpha\). On donne une condition nécessaire et suffisante pour que la perturbation par une mesure \(\geq 0\) régulière produise une fonction de Green comparable à la fonction initiale. On montre enfin que le semi-groupe du mouvement brownien et son perturbé par une mesure \(\geq 0\) radiale sont comparables si et seulement si cette mesure engendre un potentiel borné, mais qu'il n'en est plus ainsi pour une mesure non radiale.
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 554330
zbMATH Keywords: Green's function
zbMATH Keywords: Riesz kernel
zbMATH Keywords: semigroup of Brownian motion
reviewed by: Rose-Marie Hervé
MaRDI profile type: Publication
cites work: Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
cites work: Bounds for the fundamental solution of a parabolic equation
cites work: Potential theory. An analytic and probabilistic approach to balayage
cites work: Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces
cites work: Q4041031
cites work: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
cites work: Conditions n�cessaires et suffisantes d'existence de r�solvantes
cites work: Uniform bounds for quotients of Green functions on \(C^{1,1}\)-domains
cites work: Q4732959
cites work: Perturbation des résolvantes et des semi-groupes par une mesure de Radon positive. (Perturbation of resolvents and semigroups by a positive Radon measure)
cites work: The Wiener criterion of regular points for the parabolic operator of order α
cites work: Q4059363
cites work: Q3808414
cites work: Q4141653
full work available at URL: https://doi.org/10.1007/bf01047834
OpenAlex ID: W4240419113
Recommended article: Q4316849
Recommended article: Differential and analytical properties of semigroups of operators
Recommended article: Semigroups of difference operators in spectral analysis of linear differential operators
Recommended article: Q3505951
Recommended article: Q4316851
Recommended article: Semilinear perturbation of resolvents and semigroups
Recommended article: An integro-differential operator and the associated semigroup of operators
Recommended article: Q3633865
Recommended article: Semigroups generated by ordinary differential operators in \(L^1(I)\)
Recommended article: Q4718945
description: scientific article; zbMATH DE number 554330