Asymptotics and zeros of symmetrically coherent pairs of Hermite type

Authors
  • J.J. Moreno-Balcázar
Publication date 2007
Host editors
  • S. Elaydi
  • J. Cushing
  • R. Lasser
  • A. Ruffing
  • V. Papageorgiou
  • W. van Assche
Book title Difference equations, special functions and orthogonal polynomals.
Event DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS, Munich, Germany
Pages (from-to) 378-393
Publisher World Scientific Publishing Co. Pte. Ltd.
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract
We consider the Sobolev inner product

\[
(f,g)_S = \int f(x)g(x) d\mu_0 + \lambda \int f'(x)g'(x)d\mu_1, \quad \lambda >0,
\]

where (μ0, μ1) is a symmetrically coherent pair with one of the two measures the Hermite measure. We give a survey of the analytical properties of the corresponding Sobolev orthogonal polynomials and establish a new result about the asymptotic behaviour of these Hermite-Sobolev orthogonal polynomials inside the support of the measures μ0 and μ1.

Keywords: Sobolev orthogonal polynomials; Hermite polynomials; Asymptotics; Symmetrically coherent pairs; Zeros
Document type Conference contribution
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