THE ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND A FORMULA OF BOHR-SOMMERFELD TYPE

Selfadjoint operators P(x, D) in Rn depending on a small parameter h are considered. Asymptotic formulas are established for the number of eigenvalues not exceeding MhR, where M is a sufficiently large number. R ≤ R0, and R0 is determined by P. In particular, for R = R0 an asymptotic formula is obtained which is analogous to the well-known Bohr-Sommerfeld formula for ordinary differential operators. Bibliography: 11 titles.