Category theorems for Schr\"odinger semigroups

Moacir Aloisio; Silas L. Carvalho; César R. de Oliveira

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arXiv · 1902.08362

Category theorems for Schr\"odinger semigroups

Moacir Aloisio·Silas L. Carvalho·César R. de Oliveira

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Abstract

Stimulated by the category theorems of Eisner and Ser\'eny in the setting of unitary and isometric $C_0$-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.

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BibTeX RIS

Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira. 2019-02-22. Category theorems for Schr\"odinger semigroups. https://arxiv.org/abs/1902.08362

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