Continuity properties of Schrödinger semigroups with magnetic fields

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dc.creatorBroderix, Kurt
dc.creatorHundertmark, Dirk
dc.creatorLeschke, Hajo
dc.date1998-08-13
dc.date2000-03-16
dc.date.accessioned2026-07-07T04:32:29Z
dc.date.available2026-07-07T04:32:29Z
dc.descriptionThe objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc. (N.S.) {\bf 7}, 447--526 (1982)] to non-zero vector potentials and more general configuration spaces.
dc.descriptionFinal Version, 51 pages, citation index, no figures
dc.identifierhttps://arxiv.org/abs/math-ph/9808004
dc.identifierhttp://arxiv.org/abs/math-ph/9808004
dc.identifierPublished in slightly different form in Rev. Math. Phys. Vol. 12, pp 181--225 (2000)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58207
dc.subjectMathematical Physics
dc.subjectFunctional Analysis
dc.subjectProbability
dc.subject35J10
dc.titleContinuity properties of Schrödinger semigroups with magnetic fields
dc.typetext

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