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Dirichlet forms on fractals: Poincaré constant and resistance
Authors:Shigeo Kusuoka  Zhou Xian Yin
Institution:(1) Research Institute for Mathematical Sciences, Kyoto University, 606 Kyoto, Japan;(2) Department of Mathematics, Beijing Normal University, 100875 Beijing, People's Republic of China
Abstract:Summary We study Dirichlet forms associated with random walks on fractal-like finite grahs. We consider related Poincaré constants and resistance, and study their asymptotic behaviour. We construct a Markov semi-group on fractals as a subsequence of random walks, and study its properties. Finally we construct self-similar diffusion processes on fractals which have a certain recurrence property and plenty of symmetries.Partly supported by the JSPS Program
Keywords:60 J 60
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