Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 361-368
Citer cet article
M. Otelbaev; Ya. T. Sultanaev. On the formula for the distribution of the eigenvalues of singular differential operators. Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 361-368. http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a5/
@article{MZM_1973_14_3_a5,
author = {M. Otelbaev and Ya. T. Sultanaev},
title = {On the formula for the distribution of the eigenvalues of singular differential operators},
journal = {Matemati\v{c}eskie zametki},
pages = {361--368},
year = {1973},
volume = {14},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a5/}
}
TY - JOUR
AU - M. Otelbaev
AU - Ya. T. Sultanaev
TI - On the formula for the distribution of the eigenvalues of singular differential operators
JO - Matematičeskie zametki
PY - 1973
SP - 361
EP - 368
VL - 14
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a5/
LA - ru
ID - MZM_1973_14_3_a5
ER -
%0 Journal Article
%A M. Otelbaev
%A Ya. T. Sultanaev
%T On the formula for the distribution of the eigenvalues of singular differential operators
%J Matematičeskie zametki
%D 1973
%P 361-368
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a5/
%G ru
%F MZM_1973_14_3_a5
In this note we construct exampLes of a function $q(x)$, which grows arbitrarily rapidly, and a function $q(x)$ ($c_1|x|^\alpha\le q(x)\le c_2|x|^\beta$, $\beta>\alpha>0$) such that for a Sturm–Liouville operator with the constructed potential functions $q(x)$, the classical formula for the number of eigenvalues of the operator that do not exceed $\lambda$ is not true.
