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On the eigenvalue behaviour for a class of operators related to self- similar measures on $$\mathbb{R}^ d$$. (English. Abridged French version) Zbl 0808.60038
Summary: We obtain the sharp order of growth of the eigenvalue distribution function for the operator in the Sobolev space $$H^ 1_ 0(\Omega)$$, generated by the quadratic form $$\int_ \Omega | u|^ 2 d\mu$$, where $$\Omega \subset \mathbb{R}^ d$$ is a bounded domain and $$\mu$$ is a probability self-similar fractal measure on $$\Omega$$.

MSC:
 60G18 Self-similar stochastic processes 60B05 Probability measures on topological spaces