Geodesic
The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type
Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 61-81 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Selfadjoint operators $P(x,D)$ in $R^n$, depending on a small parameter $h$ are considered. Asymptotic formulas are established for the number of eigenvalues not exceeding $Mh^R$, where $M$ is a sufficiently large number. $R\leqslant R_0$, and $R_0$ is determined by $P$. In particular, for $R=R_0$ an asymptotic formula is obtained which is analogous to the well-known Bohr–Sommerfeld formula for ordinary differential operators. Bibliography: 11 titles. 
@article{SM_1981_38_1_a4,
     author = {V. I. Feigin},
     title = {The asymptotic distribution of eigenvalues and a~formula of {Bohr{\textendash}Sommerfeld} type},
     journal = {Sbornik. Mathematics},
     pages = {61--81},
     year = {1981},
     volume = {38},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_38_1_a4/}
}
TY  - JOUR
AU  - V. I. Feigin
TI  - The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type
JO  - Sbornik. Mathematics
PY  - 1981
SP  - 61
EP  - 81
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1981_38_1_a4/
LA  - en
ID  - SM_1981_38_1_a4
ER  - 
%0 Journal Article
%A V. I. Feigin
%T The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type
%J Sbornik. Mathematics
%D 1981
%P 61-81
%V 38
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1981_38_1_a4/
%G en
%F SM_1981_38_1_a4
V. I. Feigin. The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type. Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 61-81. http://geodesic.mathdoc.fr/item/SM_1981_38_1_a4/

[1] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, izd-vo “Nauka”, Moskva, 1976 | MR

[2] A. G. Brusentsev, F. S. Rofe-Beketov, “Usloviya samosopryazhennosti silno ellipticheskikh sistem proizvolnogo poryadka”, Matem. sb., 95(137) (1974), 108–130

[3] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, izd-vo MGU, Moskva, 1965

[4] J. J. Duistermaat, “Oscillatory integrals, Lagrange immersions and unfolding of singularities”, Comm. Pure and Appl. Math., 27:2 (1974), 207–281 | DOI | MR | Zbl

[5] V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, izd-vo “Nauka”, Moskva, 1977 | MR | Zbl

[6] R. Beals, C. Feferman, “Spatially inhomogeneous pseudodifferential operators. I”, Comm. Pure and Appl. Math., 27:1 (1974), 1–24 | DOI | MR | Zbl

[7] R. Beals, “A general calculus of pseudodifferential operators”, Duke Math. J., 42:1 (1975), 1–42 | DOI | MR | Zbl

[8] V. I. Feigin, “Novye klassy psevdodifferentsialnykh operatorov v $R^n$ i nekotorye prilozheniya”, Trudy Mosk. matem. o-va, XXXVI (1978), 152–192

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

[10] V. L. Roitburd, “O kvaziklassicheskoi asimptotike spektra psevdodifferentsialnogo operatora”, Uspekhi matem. nauk, XXXI:4(185) (1976), 275–276 | MR

[11] M. A. Shubin, Psevdodifferentsialnye operatory i spektralnaya teoriya, izd-vo “Nauka”, Moskva, 1978 | MR | Zbl