English

A P.C.F. Self-Similar Set with no Self-Similar Energy

Functional Analysis 2017-01-30 v1

Abstract

A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.

Keywords

Cite

@article{arxiv.1701.07885,
  title  = {A P.C.F. Self-Similar Set with no Self-Similar Energy},
  author = {Roberto Peirone},
  journal= {arXiv preprint arXiv:1701.07885},
  year   = {2017}
}

Comments

6 pages