We define thin equivalence relations ∼ on shift spaces and derive Dirichlet forms on the quotient space 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-7, author = {Manfred Denker and Atsushi Imai and Susanne Koch}, title = {Dirichlet forms on quotients of shift spaces}, journal = {Colloquium Mathematicae}, volume = {107}, year = {2007}, pages = {57-80}, zbl = {1118.28004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-7} }
Manfred Denker; Atsushi Imai; Susanne Koch. Dirichlet forms on quotients of shift spaces. Colloquium Mathematicae, Tome 107 (2007) pp. 57-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-7/