On Reproducing Kernel Hilbert Spaces of Polynomials

Certain Hilbert spaces of polynomials, called Szegö spaces [11], are studied. A transformation, called Hilbert traneformation, is constructed for every polynomial associatted with a Szegö space. An orthogonal set is found in a Szegö space which determines the norm of the space. A matrix factorization theory is obtained for defining polynomials. Measures associated with a Szegö space are parametrized by functions which ue analytic and bounded by one in the unit disk. A fundmental factorization theorem relates Szegö spaces to weighted Hardy spaces.