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APRG Seminar

Title: The operator Fejer-Riesz theorem in two variables, I
Speaker: Michael Dritschel (Newcastle University, UK)
Date: 28 May 2024
Time: 11:30 am
Venue: LH-1, Mathematics Department

The Fejer–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.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 15 Jul 2024