On discreteness of spectrum of a functional differential operator

Labovskiy, Sergey, and Getimane, Mário Frengue. "On discreteness of spectrum of a functional differential operator." Mathematica Bohemica 139.2 (2014): 213-229. <http://eudml.org/doc/261875>.

@article{Labovskiy2014,
abstract = {We study conditions of discreteness of spectrum of the functional-differential operator \[ \mathcal \{L\} u=-u^\{\prime \prime \}+p(x)u(x)+\int \_\{-\infty \}^\infty (u(x)-u(s)) \{\rm d\}\_s r(x,s) \] 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.},
author = {Labovskiy, Sergey, Getimane, Mário Frengue},
journal = {Mathematica Bohemica},
keywords = {spectrum; functional differential operator; spectrum; functional differential operator},
language = {eng},
number = {2},
pages = {213-229},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On discreteness of spectrum of a functional differential operator},
url = {http://eudml.org/doc/261875},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Labovskiy, Sergey
AU - Getimane, Mário Frengue
TI - On discreteness of spectrum of a functional differential operator
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 213
EP - 229
AB - We study conditions of discreteness of spectrum of the functional-differential operator \[ \mathcal {L} u=-u^{\prime \prime }+p(x)u(x)+\int _{-\infty }^\infty (u(x)-u(s)) {\rm d}_s r(x,s) \] 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.
LA - eng
KW - spectrum; functional differential operator; spectrum; functional differential operator
UR - http://eudml.org/doc/261875
ER -