Representation of solutions of second order one-dimensional model hyperbolic equations

We study the Fourier-Walsh spectrum ({ widehat mu (S);S subset { 1, ldots n} } ) of the Moebius function µ restricted to {0, 1, 2, …, 2ⁿ ? 1} ? {0, 1}ⁿ and prove that it is not captured by levels ({ widehat mu (S):|S| < rho n} ), with ρ a sufficiently small constant. This improves the author’s earlier result in [B2].