On analytic factorisation of positive hermitian matrix functions over the bidisc.

Blower, Gordon (1999) On analytic factorisation of positive hermitian matrix functions over the bidisc. Linear Algebra and its Applications, 295 (1-3). pp. 149-158. ISSN 0024-3795

Abstract

Let be a positive hermitian (Ω0) matrix-valued function on the bitorus with and . 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 may be factored as FF* with F an N×∞ analytic operator function.