The Fejerâ€“Riesz thorem states that a positive (i.e., non-negative) trigonometric polynomial of degree $d$ on the unit circle is the hermitian square of an analytic polynomial of the same degree. Rosenblum extended this to polynomials with operator coefficients. The goal of these talks will be to outline a proof of a similar theorem in two variables. Since the techniques used in some proofs of the single variable case play an important role in the two variable proof, this particular talk concentrates primarily on these ideas. An application to strictly positive operator valued multivariable trigonometric polynomials is also considered.

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Last updated: 15 Jul 2024