06-32 Rafael del Rio, Olga Tchebotareva

Sturm-Liouville operators in the half axis with local perturbatins (79K, dvi, LaTex 2e) Feb 17, 06

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Abstract. We give conditions which imply equivalence of the Lebesgue measure with respect to a measure $\mu $ generated as an average of spectral measures corresponding to Sturm--Liouville operators in the half axis. We apply this to prove that some spectral properties of this operators hold for large sets of boundary conditions if and only if they hold for large sets of positive local perturbations.

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