The state density and other spectral invariants of selfadjoint elliptic operators with random coefficients
Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 185-202 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the article the existence of a state density and other spectral invariants of selfadjoint elliptic operators with random coefficients is proved. The asymptotic behavior of the state density for $\lambda\to+\infty$ is investigated. Bibliography: 15 titles.
@article{SM_1977_33_2_a1,
     author = {A. I. Gusev},
     title = {The state density and other spectral invariants of selfadjoint elliptic operators with random coefficients},
     journal = {Sbornik. Mathematics},
     pages = {185--202},
     year = {1977},
     volume = {33},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_2_a1/}
}
TY  - JOUR
AU  - A. I. Gusev
TI  - The state density and other spectral invariants of selfadjoint elliptic operators with random coefficients
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 185
EP  - 202
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1977_33_2_a1/
LA  - en
ID  - SM_1977_33_2_a1
ER  - 
%0 Journal Article
%A A. I. Gusev
%T The state density and other spectral invariants of selfadjoint elliptic operators with random coefficients
%J Sbornik. Mathematics
%D 1977
%P 185-202
%V 33
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1977_33_2_a1/
%G en
%F SM_1977_33_2_a1
A. I. Gusev. The state density and other spectral invariants of selfadjoint elliptic operators with random coefficients. Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 185-202. http://geodesic.mathdoc.fr/item/SM_1977_33_2_a1/

[1] L. A. Pastur, “Spektry sluchainykh samosopryazhennykh operatorov”, Uspekhi matem. nauk, XXVIII:1(169) (1973), 3–64 | MR

[2] M. A. Shubin, “Plotnost sostoyanii samosopryazhennykh ellipticheskikh operatorov s pochti-periodicheskimi koeffitsientami”, Trudy seminara im. I. G. Petrovskogo, 3, 1977, 243–275

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

[4] M. S. Agranovich, M. I. Vishik, “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, Uspekhi matem. nauk, XIX:3(117) (1964), 53–162

[5] S. D. Eidelman, S. D. Ivasishen, “Issledovanie matritsy Grina odnorodnoi parabolicheskoi granichnoi zadachi”, Trudy Mosk. matem. ob-va, XXIII, 1970, 179–234 | MR

[6] S. D. Eidelman, Parabolicheskie sistemy, Nauka, M., 1964 | MR

[7] V. A. Solonnikov, “O kraevykh zadachakh dlya lineinykh parabolicheskikh sistem differentsialnykh uravnenii obschego vida”, Trudy matem. in-ta im. V. A. Steklova, LXXXIII, 1965, 3–163 | MR

[8] D. Dub, Veroyatnostnye protsessy, IL, M., 1956

[9] A. A. Tempelman, “Ergodicheskie teoremy dlya obschikh dinamicheskikh sistem”, Trudy Mosk. matem. ob-va, XXVI, 1972, 95–132 | MR

[10] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[11] M. A. Shubin, “Psevdodifferentsialnye pochti-periodicheskie separatory i algebry Fon Neimana”, Trudy Mosk. matem. ob-va, XXXV, 1976, 103–163

[12] L. Khermander, “Psevdodifferentsialnye operatory i gipoellipticheskie uravneniya”, Psevdodifferentsialnye operatory, Mir, M., 1967, 297–366

[13] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Mir, M., 1967

[14] R. T. Seeley, “Analitic extension of the trace associated with elliptic boundary problems”, Amer. J. Math, 91:4 (1969), 963–983 | DOI | MR | Zbl

[15] P. T. Sili, “Stepeni ellipticheskogo operatora”, Matematika, 12:1 (1968), 96–112