Dirichlet forms on quotients of shift spaces

Manfred Denker; Atsushi Imai; Susanne Koch

doi:10.4064/cm107-1-7

Dirichlet forms on quotients of shift spaces

Manfred Denker, Atsushi Imai, Susanne Koch

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We define thin equivalence relations ~ on shift spaces A^∞ and derive Dirichlet forms on the quotient space ∑= A^∞/~ 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 Sierpinski gasket.

Original language	English (US)
Pages (from-to)	57-80
Number of pages	24
Journal	Colloquium Mathematicum
Volume	107
Issue number	1
DOIs	https://doi.org/10.4064/cm107-1-7
State	Published - 2007

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4064/cm107-1-7

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abstract = "We define thin equivalence relations \textasciitilde{} on shift spaces A∞ and derive Dirichlet forms on the quotient space ∑= A∞/\textasciitilde{} 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 Sierpinski gasket.",

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AU - Koch, Susanne

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AB - We define thin equivalence relations ~ on shift spaces A∞ and derive Dirichlet forms on the quotient space ∑= A∞/~ 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 Sierpinski gasket.

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Dirichlet forms on quotients of shift spaces

Abstract

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