Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product |
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Authors: | G. López F. Marcellán W. Van Assche |
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Affiliation: | 1. Facultad de Matemática y Cibernética, Universidad de la Habana, Habana 4, Cuba 2. Departamento de Ingeniería Escuela Politécnica Superior, Universidad Carlos III de Madrid, E-28913, Leganés, Spain 3. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001, Heverlee, Belgium
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Abstract: | We investigate the asymptotic properties of orthogonal polynomials for a class of inner products including the discrete Sobolev inner products $leftlangle {h,{text{ }}g} rightrangle = int h g dmu + sum {_{j = 1}^m } sum {_{i = 0}^{N_j } M_{j,i} h^{(i)} (c_j )} g^{(i)} (c_j )$ , where μ is a certain type of complex measure on the real line, andc j are complex numbers in the complement of supp(μ). The Sobolev orthogonal polynomials are compared with the orthogonal polynomials corresponding to the measure μ. |
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