Analytic interpolation with a degree constraint

Tryphon T. Georgiou

Research output: Contribution to journalConference articlepeer-review

Abstract

In [61], [7], [8] it was shown that there is a correspondence between nonnegative (hermitian) trigonometric polynomials of degree ≤n and solutions to the standard Nevanlinna-Pick-Caratheodory interpolation problem with n+1 constraints, which are rational and also of degree ≤n. It was conjectured that the correspondence under suitable normalization is bijective and thereby, that it results in a complete parametrization of rational solutions of degree ≤n. The conjecture was proven in an insightful work by Byrnes et. al. along with a detailed study of this parametrization. However, the result in [1] was shown under a slightly restrictive assumption that the trigonometric polynomials are positive and accordingly, the corresponding solutions have positive real part. The purpose of the present note is to extend the result to the case of nonnegative trigonometric polynomials as well. We present the arguments in the context of the general Nevanlinna-Pick-Caratheodory-Fejer interpolation.

Original languageEnglish (US)
Pages (from-to)2769-2773
Number of pages5
JournalProceedings of the IEEE Conference on Decision and Control
Volume3
StatePublished - Dec 1 1998
EventProceedings of the 1998 37th IEEE Conference on Decision and Control (CDC) - Tampa, FL, USA
Duration: Dec 16 1998Dec 18 1998

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