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