2022-01-28T06:15:25Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000402382021-03-01T21:04:32ZMarkov Property of Kusuoka-Zhou's Dirichlet Forms on Self-Similar SetsKigami, Jun138835415application/pdfThe main purpose of this note is to fill a gap in Kusuoka-Zhou's construction of self-similar Dirichlet forms on self- similar sets. Unfortunately, it is not quite clear whether or not the self-similar closed form $\E$ obtained in the proof of Theorem 6.9 of [KZ] satisfies the Markov property. We will use a kind of fixed point theorem of order preserving additive maps on a cone to prove existence of a self-similar closed form with the Markov property. The fixed point theorem will be introduced in \S 1. It is also applicable to other problems, for example, the existence problem of a harmonic structure on a p.c.f. self-similar set. In \S 2, we will apply the fixed point theorem to show existence of self-similar Dirichlet forms on self-similar sets.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2000application/pdfJournal of mathematical sciences, the University of Tokyo172733AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40238/files/jms070103.pdfeng