Criticality of Schrodinger forms and recurrence of Dirichlet forms
Criticality of Schrodinger forms and recurrence of Dirichlet forms
复制标题
薛定谔形式的临界性和狄利克雷形式的重现
DOI：
10.1090/tran/8865
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发表时间：
2023
影响因子：
1.3
通讯作者：
Uemura Toshihiro
中科院分区：
文献类型：
--
作者：
Takeda Masayoshi;Uemura Toshihiro
引入扩展薛定谔空间的概念，我们以类似于狄利克雷形式的递归和瞬态的方式定义薛定谔形式的临界性和亚临界性。我们证明，当且仅当存在相关薛定谔半群的过剩函数并且由过剩函数的变换定义的狄利克雷形式是循环的（或瞬态）时，薛定谔形式是临界的（或亚临界的）。我们根据谱底给出了薛定谔形式亚临界性的分析条件。
Introducing the notion of extended Schrödinger spaces, we define the criticality and subcriticality of Schrödinger forms in the manner similar to the recurrence and transience of Dirichlet forms. We show that a Schrödinger form is critical (resp. subcritical) if and only if there exists an excessive function of the associated Schrödinger semigroup and the Dirichlet form defined by-transform of the excessive function is recurrent (resp. transient). We give an analytical condition for the subcriticality of Schrödinger forms in terms of the bottom of spectrum.