Continuous integral kernels for unbounded Schroedinger semigroups and their spectral projections

Simple item page
dc.creatorBroderix, Kurt
dc.creatorLeschke, Hajo
dc.creatorMüller, Peter
dc.date2002-09-12
dc.date2004-07-05
dc.date.accessioned2026-07-07T04:29:25Z
dc.date.available2026-07-07T04:29:25Z
dc.descriptionBy suitably extending a Feynman-Kac formula of Simon [Canadian Math. Soc. Conf. Proc, 28 (2000), 317-321], we study one-parameter semigroups generated by (the negative of) rather general Schroedinger operators, which may be unbounded from below and include a magnetic vector potential. In particular, a common domain of essential self-adjointness for such a semigroup is specified. Moreover, each member of the semigroup is proven to be a maximal Carleman operator with a continuous integral kernel given by a Brownian-bridge expectation. The results are used to show that the spectral projections of the generating Schroedinger operator also act as Carleman operators with continuous integral kernels. Applications to Schroedinger operators with rather general random scalar potentials include a rigorous justification of an integral-kernel representation of their integrated density of states - a relation frequently used in the physics literature on disordered solids.
dc.description41 pages. Final version. Dedicated to Volker Enss on the occasion of his 60th birthday
dc.identifierhttps://arxiv.org/abs/math-ph/0209020
dc.identifierhttp://arxiv.org/abs/math-ph/0209020
dc.identifierJournal of Functional Analysis 212 (2004) 287-323
dc.identifierdoi:10.1016/j.jfa.2004.01.009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57145
dc.subjectMathematical Physics
dc.subjectFunctional Analysis
dc.subject47D08 (Primary); 47B25, 47B34 (Secondary)
dc.titleContinuous integral kernels for unbounded Schroedinger semigroups and their spectral projections
dc.typetext

Files

Collections

arXiv