On discreteness of spectrum of a functional differential operator

Title:

On discreteness of spectrum of a functional differential operator

Creator:

Labovskiy, Sergey and Getimane, Mário Frengue

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f14fdef0-1ebf-4284-b0aa-e6dccb5f5462
uuid:f14fdef0-1ebf-4284-b0aa-e6dccb5f5462
doi:10.21136/MB.2014.143850

Subject:

spectrum and functional differential operator

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

213-229

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false