Para-orthogonal polynomials and chain sequences

Abstract

Three term recurrence formula has been an important tool in the studies of orthogonal polynomials on the real line. Positive chain sequences also play an important role in these studies. In recent years we have realized that the use of a different type of three term recurrence formula in combination with the use of positive chain sequences is also very important for studying the properties of orthogonal polynomials on the unit circle. In this text we give some new connection that exists between orthogonal polynomials on the unit circle and para-orthogonal polynomials given by three term recurrence formula.