Spectral properties of birth-death polynomials

Erik A. van Doorn

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
21 Downloads (Pure)

Abstract

We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by problems and results in this stochastic setting we present necessary and sufficient conditions in terms of the parameters in the recurrence relation for the smallest or second smallest point in the support of the orthogonalizing measure to be larger than zero, and for the support to be discrete with no finite limit point.
Original languageEnglish
Pages (from-to)251-258
Number of pages8
JournalJournal of computational and applied mathematics
Volume284
DOIs
Publication statusPublished - 15 Aug 2015

Keywords

  • MSC-60J80
  • MSC-42C05
  • Spectrum
  • Orthogonal polynomials
  • Orthogonalizing measure
  • Birth-death process
  • Stieltjes moment problem

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