Carleson Measures and Logvinenko-Sereda sets on compact manifolds

TL;DR

This paper characterizes Carleson measures and Logvinenko-Sereda sets for eigenfunction spaces on compact Riemannian manifolds, advancing understanding of harmonic analysis in geometric contexts.

Contribution

It provides a new characterization of these measures and sets specifically for eigenfunction spaces on compact manifolds, extending classical results to geometric settings.

Findings

Characterization of Carleson measures on eigenfunction spaces

Description of Logvinenko-Sereda sets in the manifold context

Extension of harmonic analysis tools to Riemannian manifolds

Abstract

Given a compact Riemannian manifold $M$ of dimension $m\geq 2$, we study the space of functions of $L^2(M)$ generated by eigenfunctions of eigenvalues less than $L\geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets.