拟正则保正型过份函数的积分表示及h-结合过程的轨道性质

Representation of Excessive Functions and Some Path Properties of h-associated Processes of Quasi-regular Positivity Preserving Coercive Forms

  • 摘要: 本文讨论拟正则保正型α-过份函数的积分表示,证明拟正则保正型(εε))的任意α-过份函数u均可表示为\varepsilon_\alpha(u, v)=\int \tildev d \mu, v \in D(\varepsilon),μ是 E上的σ有限测度·并证明(ε,ε))的h-结合过程是暂留的和非保守的。

     

    Abstract: In this paper, we first give a representation of α-excessive function of quasi-regular positivity preserving coercive forms (ε,Dε)). More precisely, for any uDε), u is an α-excessive function of (ε,Dε)) if and only if there exists a unique α-finite positive measure μ on (E,βE)) such that μ dose not charge ε-exceptional sets, Dε)⊂L1E,μ) and \varepsilon_\alpha(u, v)=\int \tildev d \mu, v \in D(\varepsilon) where ~v is all ε-quasi-continuous m-version of v. Then, we prove that the h-associated processes of symmetric quasi-regular positivity preserving coercive form is transient, non-conservative and non-recurrent.

     

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