Orthogonal Polynomials on the Unit Circle with Respect to a Rational Weight Function

Abstract

We use the analogue of the Christoffel’s formula for orthogonal polynomials on the unit circle introduced in [5] to construct a system of orthogonal polynomials on the unit circle with respect to weights of the type \( \left| {\frac{{p\left( z \right)}} {{g\left( z \right)}}} \right|^2 \) , where p(z) and g(z) are arbitrary polynomials. Exact formulas are established for Toeplitz determinants of these weights.KeywordsOrthogonal polynomialsChristoffel’s formulaToeplitz determinants