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Strong Nonnegative Linearization of Orthogonal Polynomials

  • Ryszard Szwarc
Chapter
  • 1.1k Downloads
Part of the Developments in Mathematics book series (DEVM, volume 13)

Abstract

A stronger notion of nonnegative linearization of orthogonal polynomials is introduced. It requires that also the associated polynomials of any order have nonnegative linearization property. This turns out to be equivalent to a maximal principle of a discrete boundary value problem associated with orthogonal polynomials through the three term recurrence relation. The property is stable for certain perturbations of the recurrence relation. Criteria for the strong nonnegative linearization are derived. The range of parameters for the Jacobi polynomials satisfying this new property is determined.

Keywords

Orthogonal polynomials recurrence relation nonnegative linearization discrete boundary value problem 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Ryszard Szwarc
    • 1
    • 2
  1. 1.Institute of MathematicsWroclaw UniversityWroclawPoland
  2. 2.Institute of MathematicsPolish Academy of ScienceWarszawaPoland

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