English

Dirichlet forms on unconstrained Sierpinski carpets

Functional Analysis 2024-03-27 v2 Probability

Abstract

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the 1/k1/k grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.

Keywords

Cite

@article{arxiv.2104.01529,
  title  = {Dirichlet forms on unconstrained Sierpinski carpets},
  author = {Shiping Cao and Hua Qiu},
  journal= {arXiv preprint arXiv:2104.01529},
  year   = {2024}
}

Comments

39 pages, 6 figures. We divide the old version into two parts. This updated version is the first part

R2 v1 2026-06-24T00:50:02.573Z