Self-similar Dirichlet form on pillow-type carpets--a short analytic construction

TL;DR

This paper provides a concise analytic proof demonstrating the existence of self-similar Dirichlet forms on pillow-type carpets, a class of fractals including the Sierpiński carpet, expanding the mathematical understanding of these structures.

Contribution

It offers a new, self-contained analytic approach to establish self-similar Dirichlet forms on pillow-type carpets, including the Sierpiński carpet.

Findings

Existence of self-similar Dirichlet forms on pillow-type carpets confirmed.

Analytic proof simplifies previous approaches.

Includes the Sierpiński carpet as a special case.

Abstract

We give a short, self-contained analytic proof of the existence of self-similar Dirichlet forms on pillow-type carpets, a family of infinitely ramified fractals that includes the Sierpi\'nski carpet.