Stimulated by the category theorems of Eisner and Serény in the setting of unitary and isometric -semigroups on separable Hilbert spaces, we prove category theorems for Schrödinger semigroups. Specically, we show that, to a given class of Schrödinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schrödinger operators.
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Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira, Category Theorems for Schrödinger Semigroups. Z. Anal. Anwend. 39 (2020), no. 4, pp. 421–431DOI 10.4171/ZAA/1666