The spectral function asymptotics for a class of hypoelliptic operators (Q1123317)

This paper deals with the asymptotics of the spectral function e(x,y,\(\lambda)\) of a class of hypoelliptic differential operators of Hörmander's type on a compact manifold. The author proposes a formula for the first term in the asymptotic development of e(x,x,\(\lambda)\) for \(\lambda \to +\infty\) and under an additional condition - a formula for N(\(\lambda)\), \(\lambda\) \(\to \infty.\) As usual, N(\(\lambda)\) is the distribution function of the eigenvalues of the operator under consideration. The results announced here without proofs generalize some previous theorems of Metivier and the author.