Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 391-399
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M. G. Gimadislamov. A discreteness criterion for the spectrum of a quasielliptic operator. Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 391-399. http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a3/
@article{MZM_1971_9_4_a3,
author = {M. G. Gimadislamov},
title = {A~discreteness criterion for the spectrum of a~quasielliptic operator},
journal = {Matemati\v{c}eskie zametki},
pages = {391--399},
year = {1971},
volume = {9},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a3/}
}
TY - JOUR
AU - M. G. Gimadislamov
TI - A discreteness criterion for the spectrum of a quasielliptic operator
JO - Matematičeskie zametki
PY - 1971
SP - 391
EP - 399
VL - 9
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a3/
LA - ru
ID - MZM_1971_9_4_a3
ER -
%0 Journal Article
%A M. G. Gimadislamov
%T A discreteness criterion for the spectrum of a quasielliptic operator
%J Matematičeskie zametki
%D 1971
%P 391-399
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a3/
%G ru
%F MZM_1971_9_4_a3
For the spectrum of the operator $$u=\sum_{j=1}^n{(-1)^{m_j}D_j^{2m_j}u+q(x)u},$$ to be discrete, where the mj are arbitrary positive integers such that $\sum_{j=1}^n{\frac1{2m_j}<1}$, and $q(x)\ge 1$, it is necessary and sufficient that $\int\limits_K{q(x)dx\to\infty}$ , when the cube $K$ tends to infinity while preserving its dimensions.
