Kernel estimates for perturbations of positive semigroups. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Seifert, Christian
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 1007
• Page End: 1008
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410483
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>Given a positive <italic>C</italic>⁰‐semigroup <italic>T</italic>⁰ on <italic>L</italic>₂(Ω, <italic>m</italic>) with a kernel <italic>k</italic>⁰, where (Ω, <italic>m</italic>) is a σ‐finite measure space, we study a suitably perturbed semigroup <italic>T</italic> and prove existence of a kernel <italic>k</italic> for <italic>T</italic> and an estimate of the <italic>k</italic> in terms of <italic>k</italic>⁰. In this way we extend a heat kernel estimate proven by Barlow, Grigor'yan and Kumagai [4] for Dirichlet forms perturbed by jump processes. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>