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Zero location and asymptotic behavior of orthogonal polynomials of Jacobi-Sobolev

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2001
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Sociedad Colombiana de Matemáticas
Universidad Nacional de Colombia
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[EN] 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 $[-\sqrt{1 + 2C}, \sqrt{1 + 2C}]$ 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 orthogonal polynomials under certain restrictions.
[ES] Para la clase de los polinomios ortogonales mónicos de Jacobi-Sobolev probamos que el menor intervalo cerrado que contiene a sus ceros reales es $[-\sqrt{1 + 2C}, \sqrt{1 + 2C}]$, donde C es una constante explícitamente determinada. Estudiamos la distribución asintótica de tales ceros, así como también analizamos el comportamiento asintótico de los polinomios ortogonales mónicos de Jacobi-Sobolev respecto a los polinomios ortogonales mónicos de Jacobi, bajo ciertas restricciones.
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16 pages, no figures.-- MSC2000 codes: Primary 41A10, 42C05; Secondary 33C45, 46E35, 46G10.
MR#: MR2003640 (2004k:33019)
Keywords
Sobolev inner product, Orthogonal polynomials, Asymptotic behavior, Distribution of zeros
Bibliographic citation
Revista Colombiana de Matemáticas, 2001, vol. 35, n. 2, p. 77-97