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:
-
Pijeira, Héctor
Quintana, Yamilet
Urbina, Wilfredo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2001
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43779
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43779
http://bdigital.unal.edu.co/33877/
- Palabra clave:
- orthogonal polynomials
asymptotic behavior
distribution of zeros
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | 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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