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Multiplier Sequences for Laguerre bases
Stockholm University, Faculty of Science, Department of Mathematics.
2012 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

Pólya and Schur completely characterized all real-rootedness preserving linear operators acting on the standard monomial basis in their famous work from 1914. The corresponding eigenvalues are from then on known as multiplier sequences. In 2009 Borcea and Br\"and\'en gave a complete characterization for general linear operators preserving real-rootedness (and stability) via the symbol. Relying heavily on these results, in this thesis, we are able to completely characterize multiplier sequences for generalized Laguerre bases. We also apply our methods to reprove the characterization of Hermite multiplier sequences achieved by Piotrowski in 2007.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2012. , 26 p.
, Research Reports in Mathematics, ISSN 1401-5617 ; 4
Keyword [en]
stability preserving operator, orthogonal polynomials, multiplier sequences
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-83391OAI: diva2:575543
2012-12-20, 306, house 6, Kräftriket, Stockholm University, Stockholm, 13:00 (English)
Available from: 2012-12-13 Created: 2012-12-10 Last updated: 2012-12-13Bibliographically approved

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