Positive Functionals and Hessenberg Matrices
Functional Analysis
2018-06-11 v1 Complex Variables
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 offer constructive 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.
Cite
@article{arxiv.1806.03099,
title = {Positive Functionals and Hessenberg Matrices},
author = {J. -B Lasserre and Mihai Putinar},
journal= {arXiv preprint arXiv:1806.03099},
year = {2018}
}
Comments
To appear in Proc. Amer. Math. Soc