On analytic factorization of positive hermitian matrix functions over the bidisc Original Research Article

Let image be a positive hermitian (Ωgreater-or-equal, slanted0) matrix-valued function on the bitorus with image and image . Then Ω is the L1-limit of FjFj*, where Fj is a (N×Nj) rectangular bi-analytic matrix function. A continuous and strictly positive hermitian image may be factored as FF* with F an N×∞ analytic operator function.