当前位置: X-MOL 学术Mediterr. J. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Decomposition Formulae for Dirichlet Forms and Their Corollaries
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2021-01-06 , DOI: 10.1007/s00009-020-01658-5
Ali BenAmor , Rafed Moussa

We provide decompositions of symmetric Dirichlet forms into recurrent and transient parts as well as into conservative and dissipative parts, in the framework of \(\sigma \)-finite measure spaces. Combining both formulae, we write every Dirichlet form as the sum of a recurrent, dissipative, and transient-conservative Dirichlet forms. Besides, we prove that Mosco convergence preserves invariant sets and that a Dirichlet form shares the same invariants sets with its approximating Dirichlet forms \({\mathcal {E}}^{(t)}\) and \({\mathcal {E}}^{(\beta )}\). Finally, we show the equivalence between conservativeness (resp. dissipativity) of a Dirichlet form and the conservativeness (reps. dissipativity) of \({\mathcal {E}}^{(t)}\) and \({\mathcal {E}}^{(\beta )}\). The elaborated results are enlightened by some examples.



中文翻译:

Dirichlet形式的分解公式及其推论

\(\ sigma \)-有限度量空间的框架内,我们将对称Dirichlet形式分解为递归和瞬态部分,以及保守和耗散部分。结合这两个公式,我们将每个Dirichlet形式写为递归,耗散和瞬变保守Dirichlet形式的总和。此外,我们证明了Mosco收敛保留不变集,并且Dirichlet形式与其近似Dirichlet形式\({\ mathcal {E}} ^ {(t)} \)\({\ mathcal {E }} ^ {(\ beta}} \)。最后,我们证明Dirichlet形式的保守性(分别为耗散性)与\({\ mathcal {E}} ^ {(t)} \)的保守性(重复耗散性)相等,并且\({\ mathcal {E}} ^ {(\ beta}} \)。详细的结果通过一些例子得到启发。

更新日期:2021-01-06
down
wechat
bug