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ISSN 1088-6850(e) ISSN 0002-9947(p)

Harmonic calculus on fractals--A measure geometric approach II

Author(s): M. Zähle
Journal: Trans. Amer. Math. Soc. 357 (2005), 3407-3423.
MSC (2000): Primary 28A80; Secondary 42B35, 47G30, 35P20
Posted: April 27, 2005
MathSciNet review: 2146630
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Abstract: Riesz potentials of fractal measures $\mu$ in metric spaces and their inverses are introduced. They define self-adjoint operators in the Hilbert space $L_2(\mu)$ and the former are shown to be compact.

In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operator the spectral dimension coincides with the Hausdorff dimension of the underlying fractal.

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