Geodesic
Spaces of generalized smoothness on $h$-sets and related Dirichlet forms
V. Knopova 1   ; M. Zähle 1
1 Mathematical Institute University of Jena Ernst-Abbe-Platz 2 07743 Jena, Germany
Studia Mathematica, Tome 174 (2006) no. 3, pp. 277-308 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The paper is devoted to spaces of generalized smoothness on so-called $h$-sets. First we find quarkonial representations of isotropic spaces of generalized smoothness on $\mathbb{R}^n$ and on an $h$-set. Then we investigate representations of such spaces via differences, which are very helpful when we want to find an explicit representation of the domain of a Dirichlet form on $h$-sets. We prove that both representations are equivalent, and also find the domain of some time-changed Dirichlet form on an $h$-set.
DOI : 10.4064/sm174-3-4
Keywords: paper devoted spaces generalized smoothness so called h sets first quarkonial representations isotropic spaces generalized smoothness mathbb h set investigate representations spaces via differences which helpful want explicit representation domain dirichlet form h sets prove representations equivalent domain time changed dirichlet form h set

V. Knopova  1   ; M. Zähle  1

1 Mathematical Institute University of Jena Ernst-Abbe-Platz 2 07743 Jena, Germany 
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V. Knopova; M. Zähle. Spaces of generalized smoothness on $h$-sets 
and related Dirichlet forms. Studia Mathematica, Tome 174 (2006) no. 3, pp. 277-308. doi: 10.4064/sm174-3-4

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