Zero localization and asymptotic behavior of orthogonal polynomials of Jacobi-Sobolev
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Autores: Héctor Esteban Pijeira Cabrera
, Yamilet Quintana, Wilfredo Urbina Romero
- Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 35, Nº. 2, 2001, págs. 77-97
- Idioma: inglés
- Enlaces
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Resumen
In this article we consider the Sobolev orthogonal polynomials associated to the Jacobi's measure on [-1, 1]. It is proven that for the class of monic Jacobi-Sobolev orthogonal polynomials, the smallest closed interval that contains its real zeros is [-√(1+2C, √ 1+2C] with C a constant explicitly determined. The asymptotic distribution of those zeros is studied and also we analyze the asymptotic comparative behavior between the sequence of monic Jacobi-Sobolev orthogonal polynomials and the sequence of monic Jacobi ortogonal polynomials under certain restrictions.
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