Multiplier Sequences for Laguerre bases

University dissertation from Stockholm : Department of Mathematics, Stockholm University

Author: Elin Ottergren; Stockholms Universitet.; [2012]

Keywords: NATURVETENSKAP; NATURAL SCIENCES; stability preserving operator; orthogonal polynomials; multiplier sequences; matematik; Mathematics;

Abstract: 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.

  This dissertation MIGHT be available in PDF-format. Check this page to see if it is available for download.