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Dirichlet forms on quotients of shift spaces

Manfred Denker; Atsushi Imai; Susanne Koch — 2007

Colloquium Mathematicae

We define thin equivalence relations ∼ on shift spaces $^{\infty}$ and derive Dirichlet forms on the quotient space $Σ =^{\infty} / \sim$ 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.

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