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

TL;DR

This paper derives optimal asymptotic decay estimates for Laguerre and Hermite coefficients of functions with singularities, establishing convergence rates for spectral orthogonal projections.

Contribution

It introduces new asymptotic estimates using Hilb-type formulas and lemmas, improving understanding of spectral approximation for singular functions.

Findings

Established optimal decay rates for Laguerre and Hermite coefficients.

Verified the asymptotic estimates with numerous examples.

Provided convergence rate results for spectral orthogonal projections.

Abstract

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.