Optimal asymptotic analyses on Laguerre and Hermite orthogonal approximation for functions of algebraic and logarithmic regularitiesYali

Based on the Hilb-type formula and van der Corput-type lemmas, we present optimal asymptotic estimates for the decay of the Laguerre and Hermite coefficients for functions with algebraic and logarithmic singularities, which in turn yield the convergence rates of the corresponding spectral orthogonal projections. Numerous examples are provided to verify the optimality of these asymptotic results.