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Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Jacob, N.;  Knopova, V. — 2005

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07. Wentzell boundary value problem for pseudo-differential operators generating Markov processes but not satisfying the transmission condition are not well understood. Studying fractional derivatives and fractional powers of such operators gives some insights in this problem. Since an L^p – theory for such operators will provide a helpful tool we investigate the L^p –domains of certain model operators. * This work...

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

V. Knopova;  M. Zähle — 2006

Studia Mathematica

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 h-set.

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