Quasiclassical asymptotics of eigenvalues of elliptic systems of differential operators on compact manifolds (Q1311085)

On a compact manifold without boundary the following elliptic system of selfadjoint differential operators is considered: \(h^ k A_ k - \sum^{k-1}_{j = 0} h^ j A_ j + \sum^ k_{j = 1} h^ j B_ j\) where \(A_ 0 = \text{id}\) and \(A_ j\) are bounded below. The author proves an asymptotic formula as \(h \to 0\) for the number of negative eigenvalues with an estimate of the rest.