Hambly, B. M. and Metz, V. and Teplyaev, A. (2006) Selfsimilar energies on p.c.f. selfsimilar fractals. Journal of the London Mathematical Society, 74 . pp. 93112.

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Abstract
On a large class of pcf (finitely ramified) selfsimilar 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 selfsimilar 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:  29 May 2015 18:19 
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