Geodesic
Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete
Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 301-312 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An expression of the form $$ l(u)=(-1)^m\sum_{j=1}^m D_j^{2m}u+[q(x)+ir(x)]u $$ is considered. Sufficient conditions are found such that the minimum operator, formally conjugate to $l(u)$, generated by the expression and the maximum operator generated by the expression $l(u)$ in $\mathscr{L}_2(E_n)$ should coincide. It is proved that if $q(x)\to\infty$ or $q(x)+r(x)\to\infty$, $|x|\to\infty$, then the operator generated by $l(u)$ in $\mathscr{L}_2(E_n)$ has a discrete spectrum. 
@article{MZM_1968_4_3_a5,
     author = {M. G. Gimadislamov},
     title = {Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete},
     journal = {Matemati\v{c}eskie zametki},
     pages = {301--312},
     year = {1968},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a5/}
}
TY  - JOUR
AU  - M. G. Gimadislamov
TI  - Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete
JO  - Matematičeskie zametki
PY  - 1968
SP  - 301
EP  - 312
VL  - 4
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a5/
LA  - ru
ID  - MZM_1968_4_3_a5
ER  - 
%0 Journal Article
%A M. G. Gimadislamov
%T Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete
%J Matematičeskie zametki
%D 1968
%P 301-312
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a5/
%G ru
%F MZM_1968_4_3_a5
M. G. Gimadislamov. Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 301-312. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a5/