B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms
Probability
2025-07-08 v1 Classical Analysis and ODEs
Abstract
We prove that B-splines with knots satisfying assumptions of the Berry-Esseen Theorem, which correspond directly to the volumes of sections of the standard simplex, tend to the Gaussian density in any Schwartz seminorm. As a consequence, we derive some asymptotic formulas connecting Hermite and Laguerre polynomials.
Cite
@article{arxiv.2507.04507,
title = {B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms},
author = {Maciej Rzeszut and Michał Wojciechowski},
journal= {arXiv preprint arXiv:2507.04507},
year = {2025}
}