The Mathematical Institute, University of Oxford, Eprints Archive

Self-similar energies on p.c.f. self-similar fractals

Hambly, B. M. and Metz, V. and Teplyaev, A. (2006) Self-similar energies on p.c.f. self-similar fractals. Journal of the London Mathematical Society, 74 . pp. 93-112.

[img]
Preview
PDF
256Kb

Abstract

On a large class of pcf (finitely ramified) self-similar fractals with possibly little symmetry we consider the question of existence and uniqueness of a Laplace operator. By considering positive refinement weights (local scaling factors) which are not necessarily equal we show that for each such fractal, under a certain condition, there are corresponding refinement weights which support a unique self-similar Dirichlet form. As compared to previous results, our technique allows us to replace symmetry by connectivity arguments.

Item Type:Article
Subjects:O - Z > Potential theory
O - Z > Probability theory and stochastic processes
Research Groups:Stochastic Analysis Group
Oxford Centre for Industrial and Applied Mathematics
ID Code:291
Deposited By:Ben Hambly
Deposited On:02 Oct 2006
Last Modified:20 Jul 2009 14:20

Repository Staff Only: item control page