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Classifications of linear operators preserving elliptic, positive and non-negative polynomials
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 650, 67-82 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2011. Vol. 650, 67-82 p.
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URN: urn:nbn:se:su:diva-68365DOI: 10.1515/CRELLE.2011.003ISI: 000286872400003OAI: diva2:472884
authorCount :1Available from: 2012-01-04 Created: 2012-01-03 Last updated: 2012-01-04Bibliographically approved

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