A+ CATEGORY SCIENTIFIC UNIT

Dirichlet forms on quotients of shift spaces

Volume 107 / 2007

Manfred Denker, Atsushi Imai, Susanne Koch Colloquium Mathematicum 107 (2007), 57-80 MSC: Primary 28A80; Secondary 60J45, 37B10. DOI: 10.4064/cm107-1-7

Abstract

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.

Authors

  • Manfred DenkerInstitut für Mathematische Stochastik
    Universität Göttingen
    Maschmühlenweg 8-10
    D-37073
    Göttingen, Germany
    e-mail
  • Atsushi ImaiOsaka Toin Junior High School
    Hiranoya 1-1054-1
    Daito, Osaka, 5740022, Japan
    e-mail
  • Susanne KochDepartment Mathematik
    Universität Hamburg
    Bundesstr. 55
    D-20146 Hamburg, Germany
    e-mail

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