Category theorems for Schr\"odinger semigroups
Spectral Theory
2019-12-02 v2 Functional Analysis
Abstract
Stimulated by the category theorems of Eisner and Ser\'eny in the setting of unitary and isometric -semigroups on separable Hilbert spaces, we prove category theorems for Schr\"odinger semigroups. Specifically, we show that, to a given class of Schr\"{o}dinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schr\"{o}dinger operators.
Cite
@article{arxiv.1902.08362,
title = {Category theorems for Schr\"odinger semigroups},
author = {Moacir Aloisio and Silas L. Carvalho and César R. de Oliveira},
journal= {arXiv preprint arXiv:1902.08362},
year = {2019}
}
Comments
12 pages, minor corrections. To appear in Zeitschrift f\"ur analysis und ihre anwendungen