Grand Lebesgue Spaces norm estimates for eigen functions for Laplace-Beltrami operator defined on the closed compact smooth Riemannian manifolds

TL;DR

This paper establishes sharp Grand Lebesgue Space norm estimates for eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds, revealing their exponential tail decay.

Contribution

It introduces novel sharp norm estimates in Grand Lebesgue Spaces for Laplace-Beltrami eigenfunctions on compact manifolds.

Findings

Eigenfunctions have exponential tail decay.

Norm estimates are sharp and in Grand Lebesgue Spaces.

Results apply to normalized eigenfunctions on smooth manifolds.

Abstract

We derive a sharp Grand Lebesgue Space norm estimations for normalized eigen functions for the Laplace-Beltrami operator defined on the compact smooth Riemann manifold. These estimates allow us to deduce in particular the exponential decreasing tail of distribution for these eigen functions.