Dirichlet forms on the Sierpiński gasket
2004; Mathematical Sciences Publishers; Volume: 217; Issue: 1 Linguagem: Inglês
10.2140/pjm.2004.217.149
ISSN1945-5844
AutoresRobert A. Meyers, Robert S. Strichartz, Alexander Teplyaev,
Tópico(s)Theoretical and Computational Physics
ResumoWe study not necessarily self-similar Dirichlet forms on the Sierpiński gasket that can be described as limits of compatible resistance networks on the sequence of graphs approximating the gasket.We describe the compatibility conditions in detail, and we also present an alternative description, based on just 3 conductance values and the 3-dimensional space of harmonic functions.In addition, we show how to parameterize all the Dirichlet forms by a set of independent variables.
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