Classifications of linear operators preserving elliptic, positive and non-negative polynomials

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dc.creatorBorcea, Julius
dc.date2008-11-26
dc.date2009-02-04
dc.date.accessioned2026-07-07T12:37:12Z
dc.date.available2026-07-07T12:37:12Z
dc.descriptionWe characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock dualities, Hankel forms, and convolutions with non-negative measures. We also establish higher-dimensional analogs of these results. In particular, our classification theorems solve the questions raised in [9] originating from entire function theory and the literature pertaining to Hilbert's 17th problem.
dc.descriptionFinal version, to appear in J. Reine Angew. Math. (Crelle); 12 pages, no figures, LaTeX2e
dc.identifierhttps://arxiv.org/abs/0811.4374
dc.identifierhttp://arxiv.org/abs/0811.4374
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218355
dc.subjectClassical Analysis and ODEs
dc.subjectFunctional Analysis
dc.subject12D10, 12D15, 15A04, 30C15, 32A60, 46E22, 47B38
dc.titleClassifications of linear operators preserving elliptic, positive and non-negative polynomials
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