1. On discreteness of spectrum of a functional differential operator
- Creator:
- Labovskiy, Sergey and Getimane, Mário Frengue
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- spectrum and functional differential operator
- Language:
- English
- Description:
- We study conditions of discreteness of spectrum of the functional-differential operator Lu = −u ′′ + p(x)u(x) + ∫ ∞ −∞ (u(x) − u(s)) dsr(x, s) on (−∞,∞). 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public