An analog of multiplier sequences for the set of totally positive sequences
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914670488584192 |
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| author | Katkova, Olga Vishnyakova, Anna |
| author_facet | Katkova, Olga Vishnyakova, Anna |
| contents | A real sequence $(b_k)_{k=0}^\infty$ is called totally positive if all minors of the infinite matrix $ \left\| b_{j-i} \right\|_{i, j =0}^\infty$ are nonnegative (here $b_k=0$ for $k<0$). In this paper, we investigate the problem of description of the set of sequences $(a_k)_{k=0}^\infty$ such that for every totally positive sequence $(b_k)_{k=0}^\infty$ the sequence $(a_k b_k)_{k=0}^\infty$ is also totally positive. We obtain the description of such sequences $(a_k)_{k=0}^\infty$ in two cases: when the generating function of the sequence $\sum_{k=0}^\infty a_k z^k$ has at least one pole, and when the sequence $(a_k)_{k=0}^\infty$ has not more than $4$ nonzero terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An analog of multiplier sequences for the set of totally positive sequences Katkova, Olga Vishnyakova, Anna Complex Variables 30C15, 15B48, 30D15, 26C10, 30D99, 30B10 A real sequence $(b_k)_{k=0}^\infty$ is called totally positive if all minors of the infinite matrix $ \left\| b_{j-i} \right\|_{i, j =0}^\infty$ are nonnegative (here $b_k=0$ for $k<0$). In this paper, we investigate the problem of description of the set of sequences $(a_k)_{k=0}^\infty$ such that for every totally positive sequence $(b_k)_{k=0}^\infty$ the sequence $(a_k b_k)_{k=0}^\infty$ is also totally positive. We obtain the description of such sequences $(a_k)_{k=0}^\infty$ in two cases: when the generating function of the sequence $\sum_{k=0}^\infty a_k z^k$ has at least one pole, and when the sequence $(a_k)_{k=0}^\infty$ has not more than $4$ nonzero terms. |
| title | An analog of multiplier sequences for the set of totally positive sequences |
| topic | Complex Variables 30C15, 15B48, 30D15, 26C10, 30D99, 30B10 |
| url | https://arxiv.org/abs/2402.05017 |