Perturbation of Dirichlet forms by measures
type: Item
instance of: scholarly article
title: Perturbation of Dirichlet forms by measures
zbMATH Open document ID: 0861.31004
DOI: 10.1007/BF00396775
author: Yanyan Li
published in: Potential Analysis
publication date: 1997-05-19T00:00:00Z
review text: This paper studies the perturbation of Dirichlet forms \({\mathfrak h}\) by measures \(\mu\). In this paper, the authors defined the perturbed form \({\mathfrak h}-\mu_-+ \mu_+\) for \(\mu_-\) in a suitable Kato class and \(\mu_+\) absolutely continuous with respect to the capacity. The main results of the paper are: (1) if the unperturbed semigroup has \(L_p\)-\(L_q\)-smoothing properties then the perturbed semigroup also has the properties; and (2) if the unperturbed semigroup is holomorphic in \(L_1\) then, for a larger class of measures \(\mu\), the perturbed semigroup also has the same property.
reviewed by: Renming Song
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 903383
zbMATH Keywords: capacity
zbMATH Keywords: smooth measures
zbMATH Keywords: perturbation of Dirichlet forms
zbMATH Keywords: Kato class
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00396775
OpenAlex ID: W1973429304
description: scientific article; zbMATH DE number 903383