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ASYMPTOTICS AND ZEROS OF SYMMETRICALLY COHERENT PAIRS OF HERMITE TYPE

M. G. DE BRUIN

Delft Institute for Applied Mathematics, Technische Universiteit Delft, The Netherlands

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W. G. M. GROENEVELT

Korteweg-De Vries Instituut voor Wiskunde, Universiteit van Amsterdam, The Netherlands

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F. MARCELLÁN

Departamento de Matemáticas, Universidad Carlos III de Madrid, Spain

Research partially supported by Dirección General de Investigación (Ministerio de Educación y Ciencia) of Spain under grant BFM2003–06335–C03–02 and INTAS Research Network NECCA INTAS 03–51–6637.

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H. G. MEIJER

Delft Institute for Applied Mathematics, Technische Universiteit Delft, The Netherlands

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J. J. MORENO–BALCÁZAR

Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Spain

Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Spain

Research partially supported by Ministerio de Educación y Ciencia of Spain under grant MTM2005–08648–C02–01 and Junta de Andalucía (G.I. FQM 0229).

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https://doi.org/10.1142/9789812770752_0032Cited by:0 (Source: Crossref)

Abstract:

We consider the Sobolev inner product

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:

AMSC: Primary 42C05, Secondary 33C45

Difference Equations, Special Functions and Orthogonal Polynomials

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ASYMPTOTICS AND ZEROS OF SYMMETRICALLY COHERENT PAIRS OF HERMITE TYPE

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