ANALYTIC REPRODUCING KERNELS AND FACTORIZATION

This paper relates questions about factorizations of positive matrices to properties of analytic reproducing kernel Hilbert spaces. In parti cular the question of when the polynomials are dense in a reproducing kernel Hilbert space is related to the factoring of an associated posi tive matrix into the form UU where U is an upper triangular matrix. A n emphasis is placed on factorization and reproducing kernel methods a s opposed to function theoretic methods.