Spectral concentration and perturbed discrete spectra

[摘要] We examine spectral concentration for a class of Sturm-Liouville problems on [0, infinity), a typical example being y (x) + (lambda - x + cx(2))y(x) = 0. The discrete spectrum for c = 0 leads to spectral concentration in the continuous spectrum for c > 0, and we use a new formula for the spectral function to make a detailed computational investigation of the way in which spectral concentration occurs. In particular, we find that, as c decreases, spectral concentration arises first from the lowest unperturbed eigenvalue and then in turn from these eigenvalues in increasing order of size.

[发布日期] 1997-12-10

[关键词] special concentration;Sturm-Liouville problems;Prufer transformation