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.
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
@article{10_4064_cm107_1_7,
author = {Manfred Denker and Atsushi Imai and Susanne Koch},
title = {Dirichlet forms on quotients of shift spaces},
journal = {Colloquium Mathematicum},
pages = {57--80},
year = {2007},
volume = {107},
number = {1},
doi = {10.4064/cm107-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm107-1-7/}
}
TY - JOUR
AU - Manfred Denker
AU - Atsushi Imai
AU - Susanne Koch
TI - Dirichlet forms on quotients of shift spaces
JO - Colloquium Mathematicum
PY - 2007
SP - 57
EP - 80
VL - 107
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm107-1-7/
DO - 10.4064/cm107-1-7
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ID - 10_4064_cm107_1_7
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%A Manfred Denker
%A Atsushi Imai
%A Susanne Koch
%T Dirichlet forms on quotients of shift spaces
%J Colloquium Mathematicum
%D 2007
%P 57-80
%V 107
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm107-1-7/
%R 10.4064/cm107-1-7
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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
