B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms

Maciej Rzeszut; Michał Wojciechowski

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arXiv · 2507.04507

B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms

Maciej Rzeszut·Michał Wojciechowski

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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.

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Maciej Rzeszut, Michał Wojciechowski. 2025-07-06. B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms. https://arxiv.org/abs/2507.04507

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