de Bruin, M.G.

Groenevelt, W.G.M.

Marcellán, F.

Meijer, H.G.

Moreno-Balcázar, J.J.

We consider the Sobolev inner product\[(f,g)_S = \int f(x)g(x) d\mu_0 + \lambda \int f'(x)g'(x)d\mu_1, \quad \lambda &gt;0,\]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; Zero

Asymptotics and zeros of symmetrically coherent pairs of Hermite type

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