Nevanlinna-Pick interpolation in the right half-plane
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908401767809024 |
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| author | Chavan, Sameer Sahu, Chaman Kumar |
| author_facet | Chavan, Sameer Sahu, Chaman Kumar |
| contents | The Szegö-Dirichlet kernel of the right half-plane $\mathbb H_{1/2}$ is given by ${\varkappa}(s, u) = ζ(s+\overline{u}),$ $s, u \in \mathbb H_{1/2},$ where $ζ$ denotes the Riemann zeta function. We show that none of the positive integer powers of $\varkappa$ has $2$-point scalar Pick property. Nevertheless, a network realization formula for the right half-plane $\mathbb H_0$ is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nevanlinna-Pick interpolation in the right half-plane Chavan, Sameer Sahu, Chaman Kumar Functional Analysis Complex Variables Primary 46E22, Secondary 11Z05 The Szegö-Dirichlet kernel of the right half-plane $\mathbb H_{1/2}$ is given by ${\varkappa}(s, u) = ζ(s+\overline{u}),$ $s, u \in \mathbb H_{1/2},$ where $ζ$ denotes the Riemann zeta function. We show that none of the positive integer powers of $\varkappa$ has $2$-point scalar Pick property. Nevertheless, a network realization formula for the right half-plane $\mathbb H_0$ is obtained. |
| title | Nevanlinna-Pick interpolation in the right half-plane |
| topic | Functional Analysis Complex Variables Primary 46E22, Secondary 11Z05 |
| url | https://arxiv.org/abs/2505.02098 |