Geodesic
On discreteness of spectrum of a functional differential operator
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 213-229.

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We study conditions of discreteness of spectrum of the functional-differential operator \[ \mathcal {L} u=-u''+p(x)u(x)+\int _{-\infty }^\infty (u(x)-u(s)) {\rm d}_s r(x,s) \] on $(-\infty ,\infty )$. In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
DOI : 10.21136/MB.2014.143850
Classification : 34K06, 34K08, 34L05
Keywords: spectrum; functional differential operator 
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Labovskiy, Sergey; Getimane, Mário Frengue. On discreteness of spectrum of a functional differential operator. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 213-229. doi : 10.21136/MB.2014.143850. http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143850/

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