ELEMENTS OF POLYA-SCHUR THEORY IN THE FINITE DIFFERENCE SETTING
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
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.
Finite difference operators, hyperbolicity preservers, mesh
IdentifiersURN: urn:nbn:se:kth:diva-194255DOI: 10.1090/proc/13115ISI: 000384000300026ScopusID: 2-s2.0-84987845546OAI: oai:DiVA.org:kth-194255DiVA: diva2:1039508
QC 201610242016-10-242016-10-212016-10-24Bibliographically approved