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(7月21日)On a recursive construction of Dirichlet form on the Sierpinski gasket
来源: 陈黎   发布时间:2017-7-19   阅读次数:589

报告人: 邱华教授(南京大学)

题目:On a recursive construction of Dirichlet form on the Sierpinski gasket.

摘要:Let $\Gamma_n$ denote the $n$-th level Sierpinski graph of the Sierpinski gasket $K$. We consider, for any given conductance $(a_0, b_0, c_0)$ on $\Gamma_0$,  the Dirchlet form ${\mathcal E}$ on $K$ obtained from a recursive construction of compatible sequence of conductances $(a_n, b_n, c_n)$ on $\Gamma_n, n\geq 0$. We prove that there is a dichotomy situation: either $a_0= b_0 =c_0$ and  ${\mathcal E}$ is the standard Dirichlet form, or $a_0 >b_0 =c_0$ (or the two symmetric alternatives),  and  ${\mathcal E}$ is a non-self-similar Dirichlet form independent of $a_0, b_0$. The second situation has also been studied by K. Hattori, T. Hattori and Watanabe as a one-dimensional asymptotic diffusion process on the Sierpinski gasket. For the spectral property, we give a sharp estimate of the eigenvalue distribution of the associated Laplacian, which improves a similar result of Hambly and Jones. This is a jointwork with Qingsong Gu and Ka-sing Lau.

报告时间:2017年7月21日下午4:00-5:00

报告地点:欧阳纯美楼314

联系人:阮火军(ruanhj@zju.edu.cn

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