Harmonic Calculus on Fractals - A Measure Geometric Approach I |
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| Authors: | U. Freiberg M. Zähle |
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| Affiliation: | (1) Mathematical Institute, University of Jena, D-07740 Jena, Germany |
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| Abstract: | Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights. |
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| Keywords: | measure geometric Laplacian Green's function self-similar measure |
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