Concentration estimates for finite expansions of spherical harmonics on two-point homogeneous spaces via the large sieve principle

Abstract

We study the concentration problem on compact two-point homogeneous spaces for finite expansions of eigenfunctions of the Laplace–Beltrami operator using large sieve methods. We derive upper bounds for concentration in terms of the maximum Nyquist density. Our proof uses estimates of the spherical harmonics basis coefficients of certain zonal filters and an ordering result for Jacobi polynomials for arguments close to one.