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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2019

Positive Functionals and Hessenberg Matrices

Résumé

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.
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Dates et versions

hal-01806491 , version 1 (03-06-2018)

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Jean-Bernard Lasserre, Mihai Putinar. Positive Functionals and Hessenberg Matrices. Proceedings of the American Mathematical Society, 2019, 147 (3), pp.1097--1108. ⟨10.1090/proc/14266⟩. ⟨hal-01806491⟩
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