Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures
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Data
2010-11-01
Autores
de Andrade, Eliana X. L. [UNESP]
Bracciali, Cleonice Fátima [UNESP]
Castano-Garcia, Laura
Moreno-Balcazar, Juan J.
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Editor
Academic Press Inc. Elsevier B.V.
Resumo
We consider the Sobolev inner product< f, g > = integral(1)(-1)f(x)g(x)d psi((alpha,beta))(x) + integral f'(x)g'(x)d psi(x),where d psi((alpha,beta))(x) = (1 = x)(alpha)(1 + x)(beta)dx with alpha, beta > -1, and psi is a measure involving a rational modification of a Jacobi weight and with a mass point outside the interval (-1, 1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product on different regions of the complex plane. In fact, we obtain the outer and inner strong asymptotics for these polynomials as well as the Mehler-Heine asymptotics which allow us to obtain the asymptotics of the largest zeros of these polynomials. We also show that in a certain sense the above inner product is also equilibrated. (C) 2010 Elsevier B.V. All rights reserved.
Descrição
Palavras-chave
Orthogonal polynomials, Sobolev orthogonal polynomials, Asymptotic
Como citar
Journal of Approximation Theory. San Diego: Academic Press Inc. Elsevier B.V., v. 162, n. 11, p. 1945-1963, 2010.