Asymptotic expansion of the spectral function of elliptic operators inR n

Abstract

Let {Eλ} be the spectral family of the operator corresponding to a self-adjoint second-adjoint second-order elliptic differential equation or to a first-order elliptic system inR n. The coefficients of the equations are assumed to be constant in a neighborhood of infinity and trapping rays are absent. We obtain the full asymptotic expansion as λ→∞ of the kernel e 1λ (x, y) of the operator dEλ/dλ in terms of rays going from the point y into the point x.