Carleson Measures and Logvinenko-Sereda sets on compact manifolds

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.