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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2505.04225 |
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| _version_ | 1866911205080170496 |
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| author | Ma, Rourou Weigert, Julian |
| author_facet | Ma, Rourou Weigert, Julian |
| contents | In this article we investigate the property of complete monotonicity within a special family $\mathcal{F}_s$ of functions in $s$ variables involving logarithms. The main result of this work provides a linear isomorphism between $\mathcal{F}_s$ and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in $\mathcal{F}_s$ is semi-algebraic. This gives a finite time algorithm to decide whether a function in $\mathcal{F}_s$ is completely monotone |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete monotonicity of log-functions Ma, Rourou Weigert, Julian Classical Analysis and ODEs High Energy Physics - Theory Mathematical Physics 26A48, 26B35, 14P10, 44A10, 40A30, 33B15 In this article we investigate the property of complete monotonicity within a special family $\mathcal{F}_s$ of functions in $s$ variables involving logarithms. The main result of this work provides a linear isomorphism between $\mathcal{F}_s$ and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in $\mathcal{F}_s$ is semi-algebraic. This gives a finite time algorithm to decide whether a function in $\mathcal{F}_s$ is completely monotone |
| title | Complete monotonicity of log-functions |
| topic | Classical Analysis and ODEs High Energy Physics - Theory Mathematical Physics 26A48, 26B35, 14P10, 44A10, 40A30, 33B15 |
| url | https://arxiv.org/abs/2505.04225 |