R. del Rio and O. Tchebotareva
Boundary conditions of Sturm-Liouville operators with mixed spectra
(57K, dvi)

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.