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