A Remark on Pál Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle

Abstract

In this paper we study the problem of explicit representation and convergence of Pál type (0;1) interpolation and its converse, with some additional conditions, on the non-uniformly distributed nodes on the unit circle obtained by projecting the interlaced zeros of $P_n(x)$ and $P′_n(x)$ on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and Pál type interpolations on non-uniformly distributed zeros on the unit circle.