- 03-381 R. del Rio and O. Tchebotareva
- Boundary conditions of Sturm-Liouville operators with mixed spectra
Aug 22, 03
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Abstract. We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence conditions are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.