Year: 2018
Type: preprint
Abstract: We study Dirichlet forms and Laplacians on self-similar sets with overlaps. A notion of "finitely ramified of finite type($f.r.f.t.$) nested structure" for self-similar sets is introduced. It allows us to reconstruct a class of self-similar sets in a graph-directed manner by a modified setup of Mauldin and Williams, which satisfies the property of finite ramification. This makes it possible to extend the technique developed by Kigami for analysis on $p.c.f.$ self-similar sets to this more general framework. Some basic properties related to $f.r.f.t.$ nested structures are investigated. Several non-trivial examples and their Dirichlet forms are provided.
Source: arXiv (Cornell University)
Authors: Cao, Shiping, Qiu, Hua
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2811048157