一个随机分形上的调和分析

A Harmonic Calculus on a Random Fractal

设ξ＝｛ξｎ，ｎ≥１｝为一独立同分布随机变量序列，Ｐ（ξ１＝２）＝ρ，Ｐ（ξ１＝３）＝１－ρ．文献［１，２］分别讨论了分形ＳＧ（Ｎ，２）和ＳＧ（２，３）上的调和分析问题．本文讨论随机分形集ＳＧ（２，ξ）上的调和函数，Ｄｉｒｉｃｈｌｅｔ问题解的存在唯一性等问题．

Let ξ= {ξn;n≥1} be a series of i. i. d random variables,P(ξ1= 2)=ρ,P(ξ1= 3) =1 - ρ. Kingami[1] and Li Junping[2] discussed harmonic Calculus on NSierpinski spaces and on SG(2, 3). In this paper,We discuss harmonic Calculus on random fractal SG(2,ξ), and existence and uniqueness of the solution to Dirichlet problem.