On the concentration of the Fourier coefficients for products of Laplace-Beltrami eigenfunctions on real-analytic manifolds

Philippe Charron, François Pagano

On a closed analytic manifold $(M,g)$, let ${\varphi }_i$ be the eigenfunctions of ${\Delta }_g$ with eigenvalues ${\lambda }_i^2$ and let $f:=\prod {\varphi }_{k_j}$ be a finite product of Laplace-Beltrami eigenfun…