The asymptotic distribution of eigenvalues and a~formula of Bohr--Sommerfeld type
Sbornik. Mathematics, Tome 38 (1981) no. 1, pp. 61-81

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

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--Sommerfeld} type},
     journal = {Sbornik. Mathematics},
     pages = {61--81},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {1981},
     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
PB  - mathdoc
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
%I mathdoc
%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/