ON REPRODUCING KERNEL HILBERT-SPACES OF POLYNOMIALS

Certain Hilbert spaces of polynomials, called Szego spaces [II], are s tudied. A transformation, called Hilbert transformation, is constructe d for every polynomial associated with a Szego space. An orthogonal se t is found in a Szego space which determines the norm of the space. A matrix factorization theory is obtained for defining polynomials. Meas ures associated with a Szego space are parametrized by functions which are analytic and bounded by one in the unit disk. A fundamental facto rization theorem relates Szego spaces to weighted Hardy spaces.