Geodesic
Estimates of the spectrum of compact pseudodifferential operators in unbounded domains
Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 431-443 
A. S. Andreev. Estimates of the spectrum of compact pseudodifferential operators in unbounded domains. Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 431-443. http://geodesic.mathdoc.fr/item/SM_1991_70_2_a6/
@article{SM_1991_70_2_a6,
     author = {A. S. Andreev},
     title = {Estimates of the spectrum of compact pseudodifferential operators in unbounded domains},
     journal = {Sbornik. Mathematics},
     pages = {431--443},
     year = {1991},
     volume = {70},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_2_a6/}
}
TY  - JOUR
AU  - A. S. Andreev
TI  - Estimates of the spectrum of compact pseudodifferential operators in unbounded domains
JO  - Sbornik. Mathematics
PY  - 1991
SP  - 431
EP  - 443
VL  - 70
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1991_70_2_a6/
LA  - en
ID  - SM_1991_70_2_a6
ER  - 
%0 Journal Article
%A A. S. Andreev
%T Estimates of the spectrum of compact pseudodifferential operators in unbounded domains
%J Sbornik. Mathematics
%D 1991
%P 431-443
%V 70
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1991_70_2_a6/
%G en
%F SM_1991_70_2_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the spectrum of compact selfadjoint pseudodifferential operators with matrix symbol in unbounded sets in Euclidean space. Two-sided bounds for the spectrum are obtained by the variational method. Additional regularity assumptions on the symbol lead to a formula for the spectral asymptotics with a remainder term estimate.

[1] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra psevdodifferentsialnykh operatorov s anizotropno-odnorodnymi simvolami”, Vestn. LGU, 1977, no. 13, 13–21 ; 1979, no. 13, 5–10 | MR | Zbl | MR | Zbl

[2] Levendorskii S. Z., “Metod priblizhennogo spektralnogo proektora”, Izv. AN SSSR. Ser. matem., 49 (1985), 1177–1227 | MR

[3] Dauge M., Robert D., “Formula de Weyl pour une classe d'operators pseudodifferentiels d'ordre negatif sur $L^2(R^n)$”, Comptes rendus Acad. sci. Ser. 1, 302:5 (1986), 175–178 | MR | Zbl

[4] Dauge M., Robert D., “Weyl's formula for a class of pseudodifferential operators with negative order on $L^2(R^n)$”, Lect Notes Math., 1256 (1987), 91–122 | DOI | MR | Zbl

[5] Andreev A. S., “Asimptotika spektra kompaktnykh psevdodifferentsialnykh operatorov na evklidovom mnozhestve”, Matem. sb., 137(179) (1988), 202–223 | MR

[6] Birman M. Sh., Solomyak M. Z., “Kolichestvennyi analiz v teoremakh vlozheniya Soboleva i prilozheniya k spektralnoi teorii”, X matem. shkola, Naukova dumka, Kiev, 1974, 5–189 | MR