A type of mean-value interpolation of holomorphic functions on an annulus

Abstract

We study mean-value interpolation of Hermite type by a polynomial of degree $m$ in $z^{-1}$ and $n$ in $z$. We show that the interpolation problem corresponding to the integrals over the segments of the form $\{t e^{i\theta}: \rho\leq t\leq 1\}$ always has a unique solution. We point out that the sequence of interpolation functions of a holomorphic function in a neighborhood of a closed annulus converges uniformly to the function when the angles that define the line segments are equally spaced.