| Abstrakt: |
Abstract: 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)) d_s r(x,s) on (-\infty,\infty). In the absence of the integral term this operator is a one-dimensional Schrodinger 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. |
