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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.08447 |
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| _version_ | 1866908599709597696 |
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| author | Khasnis, Mandar Sholapurkar, V. M. |
| author_facet | Khasnis, Mandar Sholapurkar, V. M. |
| contents | In this article, we study some special cases of the problem of classifying polynomials $p:\mathbb{R}^2_+\to (0,\infty)$ for which the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+}$ is a completely monotone net, where $p(x,y)=b(x)+a(x)y$, $a(x)$ and $b(x)$ are polynomials with $deg(a) < deg (b)$. We also give examples of $a(x)$ and $b(x)$ such that the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+}$ is not completely monotone. Furthermore, we also study some properties of the associated subnormal weighted $2$-shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint Complete Monotonicity of reciprocal of a polynomial in two variables Khasnis, Mandar Sholapurkar, V. M. Functional Analysis 44A60 In this article, we study some special cases of the problem of classifying polynomials $p:\mathbb{R}^2_+\to (0,\infty)$ for which the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+}$ is a completely monotone net, where $p(x,y)=b(x)+a(x)y$, $a(x)$ and $b(x)$ are polynomials with $deg(a) < deg (b)$. We also give examples of $a(x)$ and $b(x)$ such that the net $\{\frac{1}{p(m,n)}\}_{m,n\in \mathbb{Z}_+}$ is not completely monotone. Furthermore, we also study some properties of the associated subnormal weighted $2$-shifts. |
| title | Joint Complete Monotonicity of reciprocal of a polynomial in two variables |
| topic | Functional Analysis 44A60 |
| url | https://arxiv.org/abs/2506.08447 |