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New multiplier sequences via discriminant amoebae,
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Moscow Mathematical Journal, ISSN 1609-3321, no 08-580 129 24Article in journal (Refereed) Published
Abstract [en]

In the classical paper \cite {PS}  I.~Schur and G.~Pol\'ya introduced and characterized two types of multiplier sequences, i.e. linear operators acting diagonally in the monomial basis of $\bR[x]$ and sending real-rooted (resp. with all real  roots of the same sign)  polynomials  to real-rooted polynomials. Motivated by a fundamental property   of amoebae and  discriminants discovered in \cite{GKZ}  we introduce below a new class of  {\em sign-independently} real-rooted polynomials and describe   diagonal operators preserving   the latter set.  A  pleasant  circumstance in our description  is that this class of diagonal operators  essentially coincides with the class of all log-concave sequences. 

Place, publisher, year, edition, pages
Stockholm, 2011. no 08-580 129 24
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-70357OAI: diva2:480680
Boris Shapiro
Available from: 2012-12-13 Created: 2012-01-19 Last updated: 2012-12-13Bibliographically approved

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