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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
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