Derivatives of the spectral function and Sobolev norms of eigenfunctions on a closed Riemannian manifold (Q1888175)

The paper deals with the spectral function and with the unit spectral projection operator, with respect to the Laplace-Beltrami operator on a closed Riemannian manifold. It generalizes the result of Hörmander on the one-term asymptotic expansion of the spectral function to derivatives of the spectral function. Moreover, it extends sharp estimates of the spectral projection operator. Some applications to spherical harmonics are presented.