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Eigenvalue Approximation for Krein-Feller-Operators

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arxiv 1903.00215 v1 pith:6PZNZOFG submitted 2019-03-01 math.SP math.CA

Uta Freiberg , Lenon Minorics This is my paper
classification math.SPmath.CA
keywords eigenvaluesbehaviorfunctionskrein-feller-operatorslimitingmeasuresapproximationcantor
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We study the limiting behavior of the eigenvalues of Krein-Feller-Operators with respect to weakly convergent probability measures. Therefore, we give a representation of the eigenvalues as zeros of measure theoretic sine functions. Further, we make a proposition about the limiting behavior of the previously determined eigenfunctions. With the main results we finally determine the speed of convergence of eigenvalues and -functions for sequences which converge to invariant measures on the Cantor set.

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