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Item type:Publication, Access status: without files , Note on basic features of large time behaviour of heat kernelsLarge time behaviour of heat semigroups (and, more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups. This framework encompasses all irreducible semigroups coming from Dirichlet forms as well as suitable perturbations thereof. It includes, in particular, Laplacians on connected manifolds, metric graphs and discrete graphs.Publicationtype: Journal Article73 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A weak Gordon type condition for absence of eigenvalues of one-dimensional Schrödinger operatorsWe study one-dimensional Schrödinger operators with complex measures as potentials and present an improved criterion for absence of eigenvalues which involves a weak local periodicity condition. The criterion leads to sharp quantitative bounds on the eigenvalues. We apply our result to quasiperiodic measures as potentials.Publicationtype: Journal Article54 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An improved criterion for absence of eigenvalues of one-dimensional Schrödinger operatorsPublicationtype: Journal Article42