Browsing by Subject "asymptotics of eigenvalues"

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Access status: Open Access ,
Eigenvalue asymptotics for the Sturm-Liouville operator with potential having a strong local negative singularity
(2017) Nursultanov, Medet; Rozenblioum, Grigori
We find asymptotic formulas for the eigenvalues of the Sturm-Liouville operator on the finite interval, with potential having a strong negative singularity at one endpoint. This is the case of limit circle in H. Weyl sense. We establish that, unlike the case of an infinite interval, the asymptotics for positive eigenvalues does not depend on the potential and it is the same as in the regular case. The asymptotics of the negative eigenvalues may depend on the potential quite strongly, however there are always asymptotically fewer negative eigenvalues than positive ones. By unknown reasons this type of problems had not been studied previously.
Access status: Open Access ,
Multipoint normal differential operators of first order
(2009) Ismailov, Zameddin I.
In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.