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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2406.13291 |
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| _version_ | 1866911135157977088 |
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| author | Bhattacharjee, Monojit Nailwal, Rajkamal |
| author_facet | Bhattacharjee, Monojit Nailwal, Rajkamal |
| contents | In this article, we characterize completely alternating functions on an abelian semigroup $S$ in terms of completely monotone functions on the product semigroup $S\times \mathbb Z_+$. We also discuss completely alternating sequences induced by a class of rational functions and obtain a set of sufficient conditions (in terms of it's zeros and poles) to determine them. As an application, we show a complete characterization of several classes of completely monotone functions on $\mathbb Z_+^2$ induced by rational functions in two variables. We also derive a set of necessary conditions for the complete monotonicity of the sequence $\{\prod_{i=1}^{k}\frac{(n+a_i)}{(n+b_i)}\}_{n \in \mathbb Z_+}, a_i, b_i \in (0,\infty)$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of completely alternating functions Bhattacharjee, Monojit Nailwal, Rajkamal Functional Analysis 44A60 In this article, we characterize completely alternating functions on an abelian semigroup $S$ in terms of completely monotone functions on the product semigroup $S\times \mathbb Z_+$. We also discuss completely alternating sequences induced by a class of rational functions and obtain a set of sufficient conditions (in terms of it's zeros and poles) to determine them. As an application, we show a complete characterization of several classes of completely monotone functions on $\mathbb Z_+^2$ induced by rational functions in two variables. We also derive a set of necessary conditions for the complete monotonicity of the sequence $\{\prod_{i=1}^{k}\frac{(n+a_i)}{(n+b_i)}\}_{n \in \mathbb Z_+}, a_i, b_i \in (0,\infty)$ |
| title | A characterization of completely alternating functions |
| topic | Functional Analysis 44A60 |
| url | https://arxiv.org/abs/2406.13291 |