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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 4, 2020, pp. 421–431
DOI: 10.4171/ZAA/1666

Published online: 2020-10-22

Category Theorems for Schrödinger Semigroups

Moacir Aloisio[1], Silas L. Carvalho[2] and César R. de Oliveira[3]

(1) Universidade Federal do Amazonas, Manaus, Brazil
(2) Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
(3) Universidade Federal de São Carlos, Brazil

Stimulated by the category theorems of Eisner and Serény in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schrödinger semigroups. Speci cally, 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.

Keywords: Schrödinger semigroups, stable $C_0$-semigroups, exponential stability, Baire category theorem

Aloisio Moacir, Carvalho Silas, de Oliveira César: Category Theorems for Schrödinger Semigroups. Z. Anal. Anwend. 39 (2020), 421-431. doi: 10.4171/ZAA/1666