On the approximation properties of Stieltjes polynomials
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908437918515200 |
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| author | Cora, Víctor Tojo, F. Adrián F. |
| author_facet | Cora, Víctor Tojo, F. Adrián F. |
| contents | We introduce and study the approximation properties of $g$-polynomials, defined as linear combinations of iterated Stieltjes integrals of a constant function. Focusing on the case where the derivator $g$ has finitely many discontinuities, we prove that the space of $g$-polynomials is dense in the space of uniformly $g$-continuous functions. This result establishes a Weierstrass-type approximation theorem within the framework of Stieltjes calculus. The characterization of the closure of the space of $g$-polynomials in the general case, where the derivator may exhibit more complex behavior, remains an open and challenging problem, which we briefly discuss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the approximation properties of Stieltjes polynomials Cora, Víctor Tojo, F. Adrián F. Classical Analysis and ODEs 26A42, 41A10, 26C99 We introduce and study the approximation properties of $g$-polynomials, defined as linear combinations of iterated Stieltjes integrals of a constant function. Focusing on the case where the derivator $g$ has finitely many discontinuities, we prove that the space of $g$-polynomials is dense in the space of uniformly $g$-continuous functions. This result establishes a Weierstrass-type approximation theorem within the framework of Stieltjes calculus. The characterization of the closure of the space of $g$-polynomials in the general case, where the derivator may exhibit more complex behavior, remains an open and challenging problem, which we briefly discuss. |
| title | On the approximation properties of Stieltjes polynomials |
| topic | Classical Analysis and ODEs 26A42, 41A10, 26C99 |
| url | https://arxiv.org/abs/2507.05080 |