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Positive Functionals and Hessenberg Matrices

Lookup NU author(s): Professor Mihai Putinar

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by American Mathematical Society , 2019.

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Abstract

Not every positive functional defined on bi-variate polynomials of a prescribed degree bound is represented by the integration against a positive measure. We isolate a couple of conditions filling this gap, either by restricting the class of polynomials to harmonic ones, or imposing the vanishing of a defect indicator. Both criteria offerconstructive cubature formulas and they are obtained via well known matrix analysis techniques involving either the dilation of a contractive matrix to a unitary one or the specific structure of the Hessenberg matrix associated to the multiplier by the underlying complex variable.

Publication metadata

Author(s): Lasserre J-B, Putinar M

Publication type: Article

Publication status: Published

Journal: Proceedings of the American Mathematical Society

Year: 2019

Volume: 147

Issue: 3

Pages: 1097-1108

Online publication date: 16/11/2018

Acceptance date: 31/05/2018

Date deposited: 14/06/2018

ISSN (print): 0002-9939

ISSN (electronic): 1088-6826

Publisher: American Mathematical Society

URL: https://doi.org/10.1090/proc/14266

DOI: 10.1090/proc/14266

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