Definiteness of certain differential operators obtained via moment expansion of non‐negative functions

Abstract

Lower bounds are demonstrated for a specific quotient of differences of Taylor polynomials of functions whose inverse Fourier transform is non-negative and additionally may be isotropic or decreasing. This provides insight on the spectra of differential operators obtained by using truncated moment expansions, especially their definiteness. Physical applications include the approximation of nonlocal elasticity or nonlocal electrostatics by gradient theories, and the Kramers-Moyal expansion.