Domain of validity of Szegِ quadrature formulas

As is well known, the n-point Szegö quadrature formula integrates correctly any Laurent polynomial in the subspace span{ 1 / z n - 1 , … , 1 / z , 1 , z , … , z n - 1 } . In this paper we enlarge this subspace. We prove that a set of 2 n linearly independent Laurent polynomials are integrated correctly. The obtained result is used for the construction of Szegö quadrature formulas. Illustrative examples are given.