Average growth of the spectral function on a Riemannian manifold

Lapointe, Hugues; Polterovich, Iosif; Safarov, Yuri

Average growth of the spectral function on a Riemannian manifold

Authors

Lapointe, Hugues

Polterovich, Iosif

Safarov, Yuri

Description

We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates of the growth of the pointwise zeta-function along vertical lines in the complex plane. Some examples and open problems regarding almost periodic properties of the spectral function are also discussed.
35 pages