Nevanlinna-Pick interpolation in the right half-plane

The Szegö-Dirichlet kernel of the right half-plane ${\mathbb{H}}_{1\mathrm{/}2}$ is given by $\mathrm{\varkappa }(s,u)=\zeta (s+\bar{u}),$ $s,u\in {\mathbb{H}}_{1\mathrm{/}2},$ where $\zeta$ denotes the Riemann zeta function. We show that none of the positive integer powers of $\mathrm{\varkappa }$ has $2$-point scalar Pick property. Nevertheless, a network realization formula for the right half-plane ${\mathbb{H}}_0$ is obtained.