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.

中文翻译：

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Schrödinger半群的范畴定理

在可分希尔伯特空间的ary等距$ C_0 $-半群的背景下，通过Eisner和Serény的类别定理，我们证明了薛定ding半群的类别定理。具体来说，我们表明，对于给定的Schrödinger半群，Baire一般而言半群是强稳定的，但不是指数稳定的。我们还介绍了相应的Schrödinger算子的典型光谱性质。