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On a condition for localization of the spectrum of the Sturm-Liouville problem on the positive semi-axis. (Russian) Zbl 0591.34020

The author considers the Sturm-Liouville problem \[ y''-q(x)y+\lambda^ 2y=0,\quad y'(0)-hy(0)=0. \] It is known that the generalized spectral functions of this problem are generated by the measure \(d\mu\) in the cases: i) \(h\geq 0\), q(x)\(\geq 0\); ii) \(h<0\), \(q(x)\geq 9h^ 2/4\). In this paper the author proves that the same is true also in the case \(h<0\), \(q(x)\geq h^ 2\).
Reviewer: D.Herceg

MSC:

34L99 Ordinary differential operators
47E05 General theory of ordinary differential operators
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