Gaussian bounds for propagators perturbed by potentials

V Liskevich, H Vogt, J Voigt

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)


We develop the perturbation theory for propagators, with the objective to prove Gaussian bounds. Let U be a strongly continuous propagator, i.e. a family of operators describing the solutions of a non-autonomous evolution equation, on an Lp space, and assume that U is positive and satisfies Gaussian upper and lower bounds. Let V be a (time-dependent) potential satisfying certain Miyadera conditions with respect to U. We show that then the perturbed propagator enjoys Gaussian upper and lower bounds as well. To prepare the necessary tools, we extend the perturbation theory of strongly continuous propagators and the theory of absorption propagators.
Translated title of the contributionGaussian bounds for propagators perturbed by potentials
Original languageEnglish
Pages (from-to)245 - 277
Number of pages33
JournalJournal of Functional analysis
Volume238 (1)
Publication statusPublished - 1 Sep 2006

Bibliographical note

Publisher: Academic Press


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