“…Over the years there were many extensions to the classical theory of orthogonal polynomials on the real line (OPRL). After the influential works by Delsarte and Genin [14,15,16] and Jones et al [31] about the nowadays called paraorthogonal polynomials on the unit circle (POPUC) -in many senses the appropriate complex analog of OPRL-, this collection of polynomials and their zeros have received considerable attention from two disparate audiences, namely researchers in orthogonal polynomials and researchers in numerical linear algebra (see for instance [27,25,26,1,14,28,15,16,49,6,2,8,42,32,44,43,50,45,39,40,11,12,38,10,41,7]). It must be said that rarely in the numerical linear algebra context the name POPUC is used; however, the reader has to proceed with caution in the literature because many results on POPUC were first discovered in this framework.…”