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arXiv · 2505.02098

Nevanlinna-Pick interpolation in the right half-plane

Sameer Chavan·Chaman Kumar Sahu
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Abstract

The Szeg\"o-Dirichlet kernel of the right half-plane $\mathbb H_{1/2}$ is given by ${\varkappa}(s, u) = \zeta(s+\overline{u}),$ $s, u \in \mathbb H_{1/2},$ where $\zeta$ 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.

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Sameer Chavan, Chaman Kumar Sahu. 2025-05-04. Nevanlinna-Pick interpolation in the right half-plane. https://arxiv.org/abs/2505.02098

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