Zero localization and asymptotic behavior of orthogonal polynomials of jacobi-sobolev
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 explicit...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2001 |
| País: | Colombia |
| Recursos: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/43779 |
| Acesso em linha: | https://repositorio.unal.edu.co/handle/unal/43779 http://bdigital.unal.edu.co/33877/ |
| Access Level: | acceso abierto |
| Palavra-chave: | orthogonal polynomials asymptotic behavior distribution of zeros |
| Resumo: | 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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