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

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We 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.
Final version, to appear in J. Reine Angew. Math. (Crelle); 12 pages, no figures, LaTeX2e

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Classical Analysis and ODEs, Functional Analysis, 12D10, 12D15, 15A04, 30C15, 32A60, 46E22, 47B38

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http://salesiana.dossiersoluciones.com/handle/123456789/218355

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.4374
 http://arxiv.org/abs/0811.4374

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arXiv