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ELEMENTS OF POLYA-SCHUR THEORY IN THE FINITE DIFFERENCE SETTING
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-1055-1474
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
American Mathematical Society (AMS), 2016. Vol. 144, no 11, 4831-4843 p.
Keyword [en]
Finite difference operators, hyperbolicity preservers, mesh
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-194255DOI: 10.1090/proc/13115ISI: 000384000300026ScopusID: 2-s2.0-84987845546OAI: oai:DiVA.org:kth-194255DiVA: diva2:1039508
Note

QC 20161024

Available from: 2016-10-24 Created: 2016-10-21 Last updated: 2016-10-24Bibliographically approved

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Brändén, Petter
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