P.C.F.上的Fredholm模自相似分形及其共形几何
Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry
摘要：
目前的工作的目的是显示如何，使用相关的狄利克雷形式的微分学，它是可能的构造Fredholm模后临界有限分形的正则调和结构。模是d-可和的，可和指数d与正则调和结构的广义拉普拉斯算子的谱维数一致。非交换微积分的特征工具允许定义一个d-能量泛函，它被证明是一个自相似的共形不变量。
英文摘要：
The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are d-summable, the summability exponent d coinciding with the spectral dimension of the generalized laplacian operator associated with the regular harmonic structures. The characteristic tools of the noncommutative infinitesimal calculus allow to define a d-energy functional which is shown to be a self-similar conformal invariant.
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