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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.13903 |
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| _version_ | 1866913580529483776 |
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| author | Anand, Akash Chavan, Sameer Nailwal, Rajkamal |
| author_facet | Anand, Akash Chavan, Sameer Nailwal, Rajkamal |
| contents | We discuss the problem of classifying polynomials $p : \mathbb R^2_+ \rightarrow (0, \infty)$ for which $\frac{1}{p}=\{\frac{1}{p(m, n)}\}_{m, n \geq 0}$ is joint completely monotone, where $p$ is a linear polynomial in $y.$ We show that if $p(x, y)=a+b x+c y+d xy$ with $a > 0$ and $b, c, d \geq 0,$ then $\frac{1}{p}$ is joint completely monotone if and only if $a d - b c \leq 0.$ We also present an application to the Cauchy dual subnormality problem for toral $3$-isometric weighted $2$-shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13903 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Joint complete monotonicity of rational functions in two variables and toral $m$-isometric pairs Anand, Akash Chavan, Sameer Nailwal, Rajkamal Functional Analysis We discuss the problem of classifying polynomials $p : \mathbb R^2_+ \rightarrow (0, \infty)$ for which $\frac{1}{p}=\{\frac{1}{p(m, n)}\}_{m, n \geq 0}$ is joint completely monotone, where $p$ is a linear polynomial in $y.$ We show that if $p(x, y)=a+b x+c y+d xy$ with $a > 0$ and $b, c, d \geq 0,$ then $\frac{1}{p}$ is joint completely monotone if and only if $a d - b c \leq 0.$ We also present an application to the Cauchy dual subnormality problem for toral $3$-isometric weighted $2$-shifts. |
| title | Joint complete monotonicity of rational functions in two variables and toral $m$-isometric pairs |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2207.13903 |