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.

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## 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 |
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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 |

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