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ELEMENTS OF POLYA-SCHUR THEORY IN THE FINITE DIFFERENCE SETTING
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 3
2016 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 11, 4831-4843 p.Article in journal (Refereed) Published
Abstract [en]

The Polya-Schur theory describes the class of hyperbolicity preservers, i.e., the class of linear operators acting on univariate polynomials and preserving real-rootedness. We attempt to develop an analog of Polya-Schur theory in the setting of linear finite difference operators. We study the class of linear finite difference operators preserving the set of real-rooted polynomials whose mesh (i.e., the minimal distance between the roots) is at least one. In particular, we prove a finite difference version of the classical Hermite-Poulain theorem and several results about discrete multiplier sequences.

Place, publisher, year, edition, pages
2016. Vol. 144, no 11, 4831-4843 p.
Keyword [en]
Finite difference operators, hyperbolicity preservers, mesh
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-135216DOI: 10.1090/proc/13115ISI: 000384000300026OAI: oai:DiVA.org:su-135216DiVA: diva2:1046613
Available from: 2016-11-14 Created: 2016-11-01 Last updated: 2016-11-14Bibliographically approved

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