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Item type:Publication, Access status: with files , Weighted composition semigroups on spaces of continuous functions and their subspacesThis paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces F(Ω) of continuous functions on a Hausdorff space Ω such that the norm-topology is stronger than the compact-open topology like the Hardy spaces, the weighted Bergman spaces, the Dirichlet space, the Bloch type spaces, the space of bounded Dirichlet series and weighted spaces of continuous or holomorphic functions. It was shown by Gallardo-Gutiérrez, Siskakis and Yakubovich that there are no non-trivial norm-strongly continuous weighted composition semigroups on Banach spaces F(D) of holomorphic functions on the open unit disc D such that H∞⊂F(D)⊂B1 where H∞ is the Hardy space of bounded holomorphic functions on D and B1 the Bloch space. However, we show that there are non-trivial weighted composition semigroups on such spaces which are strongly continuous w.r.t. the mixed topology between the norm-topology and the compact-open topology. We study such weighted composition semigroups in the general setting of Banach spaces of continuous functions and derive necessary and sufficient conditions on the spaces involved, the semiflows and semicocycles for strong continuity w.r.t. the mixed topology and as a byproduct for norm-strong continuity as well. Moreover, we give several characterisations of their generator and their space of norm-strong continuity.Publicationtype: Journal Article8 82 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Spectral approximation of generalized Schrödinger Operators via approximation of subwords(Springer, 2024-01); ; ; ; We prove criteria, purely based on finite subwords of the potential, for spectral inclusion as well as Hausdorff approximation of pseudospectra or even spectra of generalized Schrödinger operators on the discrete line or half-line. In fact, our results are neither limited to Schrödinger or self-adjoint operators, nor to Hilbert space or 1D: By employing localized lower norms, we strongly generalize known results from the self-adjoint case to much more general and non-normal situations, including various configurations of Hamiltonians and further non-self-adjoint models with aperiodic or pseudoergodic potentials, even models with multiple varying diagonals and entries in a Banach space.Publicationtype: Journal ArticleScopus© Citations 1 38 46