Nevanlinna-Pick interpolation in the right half-plane

Abstract

The Szegö-Dirichlet kernel of the right half-plane ${\mathbb{H}}_{1/2}$ is given by $\varkappa (s,u)=\hat{I}\P (s+\overline{u}),$ $s,u\in {\mathbb{H}}_{1/2},$ where $\hat{I}\P$ 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.

9 Pages. Any comments or suggestions are welcome. Accepted for publication in Complex analysis and Operator theory