Derivatives of the spectral function and Sobolev norms of eigenfunctions on a closed Riemannian manifold
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.
scientific article; zbMATH DE number 2117699