Classifications of linear operators preserving elliptic, positive and non-negative polynomials
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
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  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.
IdentifiersURN: urn:nbn:se:su:diva-68365DOI: 10.1515/CRELLE.2011.003ISI: 000286872400003OAI: oai:DiVA.org:su-68365DiVA: diva2:472884
authorCount :12012-01-042012-01-032012-01-04Bibliographically approved