论文标题
基本频谱和伐木类型属性
Essential spectrum and Feller type properties
论文作者
论文摘要
我们为常规的半迪里奇莱特形式提供了必要的条件，以享受新的feller型财产，我们将其称为\ emph {弱的Feller属性}。我们的表征涉及潜在的理论和概率方面，即使在对称情况下，也似乎是新的。结果，在对称情况下，我们获得了（由诱导的）常规对称dirichlet形式和一个适用于例如在$ \ mathsf {rcd^*} $ spaces上以cheger形式。
We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy a new Feller type property, which we call \emph{weak Feller property}. Our characterization involves potential theoretic as well as probabilistic aspects and seems to be new even in the symmetric case. As a consequence, in the symmetric case, we obtain a new variant of a decomposition principle of the essential spectrum for (the self-adjoint operators induced by) regular symmetric Dirichlet forms and a Persson type theorem, which applies e.g. to Cheeger forms on $\mathsf{RCD^*}$ spaces.
