B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916829565288448 |
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| author | Rzeszut, Maciej Wojciechowski, Michał |
| author_facet | Rzeszut, Maciej Wojciechowski, Michał |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms Rzeszut, Maciej Wojciechowski, Michał Probability Classical Analysis and ODEs 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. |
| title | B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms |
| topic | Probability Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2507.04507 |