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Analysis on Graphs and Its Applications
We describe relation between analysis on fractals and the theory of self-similar groups. In particular, we focus on the construction of the Laplacian on limit sets of such groups in several concrete examples, and in the general p.c.f. case. We pose a number of open questions. Contents 1. Introduction 1 2. Self-similar groups and their limit spaces 3 3. Representations of groups and functions 13 4. Laplacians, Dirichlet forms and resistance forms 18 5. Examples of Laplacians on limit spaces 24doi:10.1090/pspum/077/2459868 fatcat:lxgxdzl4hrecdfai27gqhoub2q