Orthogonal polynomials for exponential weights xe-2Q(x) on [0,d)

Eli Levin, Doron Lubinsky

Research output: Contribution to journalArticlepeer-review

Abstract

Let I = [0, d), where d is finite or infinite. Let Wρ (x) = xρ exp (-Q (x)), where ρ > - 1/2 and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight Wρ2, obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.

Original languageEnglish
Pages (from-to)199-256
Number of pages58
JournalJournal of Approximation Theory
Volume134
Issue number2
DOIs
StatePublished - Jun 2005

Bibliographical note

Funding Information:
∗ Corresponding author. Fax: +1 404 894 4409. E-mail address: lubins ky@math.gatech.edu (D. Lubinsky). 1This author acknowledges s upport by National Science Foundation Grant DMS 0400446.

Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

Keywords

  • Exponential weights
  • Laguerre weights
  • Orthogonal polynomials

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