Geodesic
Dirichlet forms on quotients of shift spaces
Manfred Denker1 ; Atsushi Imai2 ; Susanne Koch3
1 Institut für Mathematische Stochastik Universität Göttingen Maschmühlenweg 8-10 D-37073 Göttingen, Germany
2 Osaka Toin Junior High School Hiranoya 1-1054-1 Daito, Osaka, 5740022, Japan
3 Department Mathematik Universität Hamburg Bundesstr. 55 D-20146 Hamburg, Germany
Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 57-80 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm107-1-7
Keywords: define thin equivalence relations sim shift spaces scr infty derive dirichlet forms quotient space mit sigma scr infty sim terms nearest neighbour averaging operator identify associated laplace operator conditions applied non self similar extensions sierpi ski gasket

Manfred Denker 1 ; Atsushi Imai 2 ; Susanne Koch 3

1 Institut für Mathematische Stochastik Universität Göttingen Maschmühlenweg 8-10 D-37073 Göttingen, Germany
2 Osaka Toin Junior High School Hiranoya 1-1054-1 Daito, Osaka, 5740022, Japan
3 Department Mathematik Universität Hamburg Bundesstr. 55 D-20146 Hamburg, Germany 
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Manfred Denker; Atsushi Imai; Susanne Koch. Dirichlet forms on quotients of shift spaces. Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 57-80. doi: 10.4064/cm107-1-7

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