An elementary proof of the operator Fejér-Riesz theorem with some multivariate generalisations
by
Michael Dritschel
University of Newcastle upon Tyne

The Fejér-Riesz theorem states that a positive trigonometric polynomial can be factored as the square of the modulus of an outer function. In the 1970's, Marvin Rosenblum proved a version of this theorem where the trigonometric polynomial has operator coefficients on a Hilbert space. During this talk, a proof will be given of this result which uses only elementary operator theory. The technique presented is also useful in factoring positive multivariate trigonometric polynomials, and this is discussed as well.

Date received: June 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeo-76.