A Stone-Weierstrass approximation theorem for monotone functions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912746168123392 |
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| author | Minguzzi, Ettore |
| author_facet | Minguzzi, Ettore |
| contents | We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of positive non-decreasing rational functions with non-negative coefficients can uniformly approximate all continuous non-decreasing functions on compact intervals. An explicit approximation formula of this type is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stone-Weierstrass approximation theorem for monotone functions Minguzzi, Ettore Functional Analysis Mathematical Physics General Topology We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of positive non-decreasing rational functions with non-negative coefficients can uniformly approximate all continuous non-decreasing functions on compact intervals. An explicit approximation formula of this type is provided. |
| title | A Stone-Weierstrass approximation theorem for monotone functions |
| topic | Functional Analysis Mathematical Physics General Topology |
| url | https://arxiv.org/abs/2512.03633 |