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

Autor:	Borcea, Julius
Rok vydání:	2008
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis 12D10 12D15 15A04 30C15 32A60 46E22 47B38
Druh dokumentu:	Working Paper
Popis:	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. Comment: Final version, to appear in J. Reine Angew. Math. (Crelle); 12 pages, no figures, LaTeX2e
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0811.4374 Zobrazit plný text záznamu View this record from Arxiv