Explicit Representations of Dirichlet Approximations.

A. Peyerimhoff; W.B. Jurkat; W. Kratz

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Spaces of generalized smoothness on h-sets and related Dirichlet forms

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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 ℝⁿ 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...