Category Theorems for Schrödinger Semigroups

Category Theorems for Schrödinger Semigroups

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. Specifically, we show that, to a given class of Schrödinger semigroups, Baire generically the semigroup...

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Veröffentlicht in:Zeitschrift für Analysis und ihre Anwendungen 2020-01, Vol.39 (4), p.421-431
Hauptverfasser: Aloisio, Moacir, Carvalho, Silas L., de Oliveira, César R.
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Hilbert space
Mathematical research
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Zusammenfassung: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. Specifically, 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.
ISSN:0232-2064
1661-4534
DOI:10.4171/zaa/1666