Geodesic
Asymptotics of the spectrum of linear operator pencils
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 245-266 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem $Au=tBu$ is considered in a bounded Lipschitz domain, where $A$ and are sums of a pseudodifferential operator satisfying a transmission condition and a singular Green operator, with $A$ elliptic. Under natural conditions the classical formula for the asymptotics of the spectrum is established, with an estimate of the remainder determined by the character of degeneration in ellipticity of the operator $B$. Bibliography: 18 titles. 
@article{SM_1985_52_1_a13,
     author = {S. Z. Levendorskii},
     title = {Asymptotics of the spectrum of linear operator pencils},
     journal = {Sbornik. Mathematics},
     pages = {245--266},
     year = {1985},
     volume = {52},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_1_a13/}
}
TY  - JOUR
AU  - S. Z. Levendorskii
TI  - Asymptotics of the spectrum of linear operator pencils
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 245
EP  - 266
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1985_52_1_a13/
LA  - en
ID  - SM_1985_52_1_a13
ER  - 
%0 Journal Article
%A S. Z. Levendorskii
%T Asymptotics of the spectrum of linear operator pencils
%J Sbornik. Mathematics
%D 1985
%P 245-266
%V 52
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1985_52_1_a13/
%G en
%F SM_1985_52_1_a13
S. Z. Levendorskii. Asymptotics of the spectrum of linear operator pencils. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 245-266. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a13/

[1] Kozlov V. A., “Asimptotika spektra nepoluogranichennykh ellipticheskikh sistem”, Problemy matem. analiza, 1979, no. 7, 70–83 | Zbl

[2] Kozlov V. A., “Ob otsenke ostatka v formule asimptotiki spektra nepoluogranichennykh ellipticheskikh sistem”, Vestn. LGU, seriya matem., mekh., astron., 1979, no. 19, vyp. 4, 112–114 | MR

[3] Kozlov V. A., “Otsenki ostatka v formulakh asimptotiki spektra dlya lineinykh operatornykh puchkov”, Funkts. analiz, 17:2, vyp. 2 (1983), 80–81. | MR | Zbl

[4] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra differentsialnykh uravnenii”, Itogi nauki. Matematicheskii analiz, 14, VINITI, M., 1977, 5–54 | MR

[5] Ivrii V. Ya., “Ob asimptotike sobstvennykh znachenii dlya odnogo klassa ellipticheskikh operatorov, deistvuyuschikh v rassloeniyakh nad mnogoobraziem s kraem”, DAN SSSR, 263:3 (1982), 530–532 | MR

[6] Tulovskii V. V., Shubin M. A., “Ob asimptoticheskom raspredelenii sobstvennykh znachenii psevdodifferentsialnykh operatorov v $R^n$”, Matem. sb., 92(134) (1973), 571–586 | MR

[7] Feigin V. I., “Asimptoticheskoe raspredelenie sobstvennykh chisel dlya gipoellipticheskikh sistem v $R^n$”, Matem. sb., 99(141) (1976), 594–614 | MR | Zbl

[8] Feigin V. I., “O spektralnoi asimptotike dlya kraevykh zadach i asimptotike otritsatelnogo spektra”, DAN SSSR, 232:6 (1977), 1269–1272 | MR

[9] Bezyaev V. I., “Asimptotika sobstvennykh znachenii gipoellipticheskikh operatorov na zamknutom mnogoobrazii”, Matem. sb., 117(159) (1982), 161–180 | MR | Zbl

[10] Levendorskii S. Z., “Ob odnom obschem metode issledovaniya asimptotiki spektra i ego primenenii k teorii obolochek”, DAN SSSR, 266:2 (1982), 276–280 | MR | Zbl

[11] Levendorskii S. Z., “Asimptoticheskoe raspredelenie sobstvennykh znachenii”, Izv. AN SSSR. Seriya matem., 46 (1982), 810–852 | MR | Zbl

[12] Shubin M. A., Psevdodifferentsialnye operatory i spektralnaya teoriya, Nauka, M., 1978 | MR

[13] Boutet de Monvel, “Boundary problems for pseudodifferential operators”, Acta math., 1971, no. 126, 11–51 | MR | Zbl

[14] Pleyel A., “Certain indefinite differential eigenvalue problems – the asymptotic distribution of their eigenfunctions”, Partial Differential Equations and Continuum Mech., Wisconsin Press, Madison, 1961, 19–37 | MR

[15] Kannai Y., “On the asymptotic behaviour of resolvent kernels, spectral functions and eigenvalues of semi-elliptic systems”, Ann. Scuqla Norm. Super. Pisa Sci. fis. e mat., 23:4 (1969), 563–634 | MR | Zbl

[16] Grubb G., “Estimation du reste dans l'ètude des valeurs propres des problemes aux limites pseudodifferentiels auto-adjoints”, C. R. Acad. Sci., 287, Sér. A (1978), 1017–1020 | MR | Zbl

[17] Hörmander L., “On the asymptotic distribution of the eigenvalues of pseudodifferential operators in $R^n$”, Ark. mat., 17:2 (1979), 297–313 | DOI | MR | Zbl

[18] Hörmander L., “The Weyl calculus of pseudodifferential operators”, Comm. Pure Appl. Math., 32 (1979), 359–443 | DOI | MR | Zbl