Domain of validity of Szegö quadrature formulas

As is well known, the n  -point Szegö quadrature formula integrates correctly any Laurent polynomial in the subspace span{1/zn-1,…,1/z,1,z,…,zn-1}1/zn-1,…,1/z,1,z,…,zn-1}. In this paper we enlarge this subspace. We prove that a set of 2n2n linearly independent Laurent polynomials are integrated correctly. The obtained result is used for the construction of Szegö quadrature formulas. Illustrative examples are given.