M.G. de Bruin
- Asymptotics and zeros of symmetrically coherent pairs of Hermite type
- DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS, Munich, Germany
- Book/source title
- Difference equations, special functions and orthogonal polynomals.
- Pages (from-to)
- World Scientific Publishing Co. Pte. Ltd.
- Document type
- Conference contribution
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
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
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