Dirichlet forms on quotients of shift spaces
Volume 107 / 2007
Colloquium Mathematicum 107 (2007), 57-80
MSC: Primary 28A80; Secondary 60J45, 37B10.
DOI: 10.4064/cm107-1-7
Abstract
We define thin equivalence relations $\sim$ on shift spaces ${\scr A}^{\infty}$ and derive Dirichlet forms on the quotient space ${\mit\Sigma} ={\scr A}^{\infty}/{\sim}$ in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.
