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

2020/04/06 by Jaming, Philippe, Speckbacher, Michael
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2004.02474

Abstract

We study the concentration problem on compact two-point homogeneous spaces of 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.

Related

• Concentration estimates for band-limited spherical harmonics expansions\n via the large sieve principle
• Problems related to the concentration of eigenfunctions
• Local spectral density and Slepian concentration for spherical Fourier-Bessel truncation spaces
• Deterministic guarantees for L¹-reconstruction: A large sieve approach with geometric flexibility
• Concentration of measure on spheres and related manifolds