Geodesic
Multidimensional spectral asymptotics for elliptic operators in a~bounded domain
Izvestiya. Mathematics , Tome 24 (1985) no. 1, pp. 49-71.

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

In this paper the author obtains high-frequency asymptotics of the trace of the product of a pair of spectral projections of elliptic operators in a bounded domain and of a number of similar expressions. Applications are given to the asymptotics' of the joint spectrum of a pair of commuting operators, to reducibility, and to quasiclassical asymptotics of the spectrum of an elliptic operator. Bibliography: 11 titles. 
@article{IM2_1985_24_1_a1,
     author = {S. M. Kozlov},
     title = {Multidimensional spectral asymptotics for elliptic operators in a~bounded domain},
     journal = {Izvestiya. Mathematics },
     pages = {49--71},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_24_1_a1/}
}
TY  - JOUR
AU  - S. M. Kozlov
TI  - Multidimensional spectral asymptotics for elliptic operators in a~bounded domain
JO  - Izvestiya. Mathematics 
PY  - 1985
SP  - 49
EP  - 71
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1985_24_1_a1/
LA  - en
ID  - IM2_1985_24_1_a1
ER  - 
%0 Journal Article
%A S. M. Kozlov
%T Multidimensional spectral asymptotics for elliptic operators in a~bounded domain
%J Izvestiya. Mathematics 
%D 1985
%P 49-71
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1985_24_1_a1/
%G en
%F IM2_1985_24_1_a1
S. M. Kozlov. Multidimensional spectral asymptotics for elliptic operators in a~bounded domain. Izvestiya. Mathematics , Tome 24 (1985) no. 1, pp. 49-71. http://geodesic.mathdoc.fr/item/IM2_1985_24_1_a1/

[1] Lifshits I. M., Gredeskul S. A., Pastur L. A., Vvedenie v teoriyu neuporyadochennykh sistem, Nauka, M., 1982 | MR

[2] Shubin M. A., “Plotnost sostoyanii samosopryazhennykh ellipticheskikh operatorov s pochti periodicheskimi koeffitsientami”, Trudy sem. im. I. G. Petrovskogo, no. 3, 1978, 243–275 | MR | Zbl

[3] Kozlov S. M., “Mnogomernye spektralnye asimptotiki dlya ellipticheskikh operatorov”, Dokl. AN SSSR, 268:4 (1983), 789–793 | MR | Zbl

[4] Colin de Verdiere Y., “Spectre conjoint d'operateurs pseudo-differentiels qui commutent”, Duke Math. Journal, 46 (1979), 169–182 | DOI | MR | Zbl

[5] Vladimirov V. S., “Mnogomernoe obobschenie tauberovoi teoremy Khardi i Littlvuda”, Izv. AN SSSR. Ser. matem., 40:5 (1976), 1084–1100 | MR

[6] Drozhzhinov Yu. N., Zavyalov B. I., “Tauberovy teoremy dlya obobschennykh funktsii s nositelyami v konusakh”, Matem. sb., 108 (1979), 78–90 | MR | Zbl

[7] Seeley R., “Norms and domains of complex powers $A_{B^z}$”, Amer. Journal of Math., 93 (1971), 299–309 | DOI | MR | Zbl

[8] Grisvard P., “Caractérisation de quelques espaces d'interpolation”, Ark. Rat. Mech. Anal., 2 (1967), 40–63 | DOI | MR

[9] Eidelman S. D., Ivasishin S. D., “Issledovanie matritsy Grina odnorodnoi parabolicheskoi granichnoi zadachi”, Trudy MMO, 23, 1970, 179–234 | MR

[10] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[11] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968