The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type

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.
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