薛定谔半群的范畴定理
Category theorems for Schrödinger semigroups
摘要：
在可分希尔伯特空间上酉和等距$C_0$ -半群的背景下，受Reinner和Serény范畴定理的启发，我们证明了Schr dinger半群的范畴定理.具体地说，我们证明了对于给定的薛定谔半群，Baire一般是强稳定的但不是指数稳定的.我们还提出了相应的薛定谔算子的一个典型的谱性质。
英文摘要：
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.
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