On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients

Herbert Dueñas Ruiz; Francisco Marcellán; Alejandro Molano

doi:10.15446/recolma.v53n2.85524

Publicado

2019-07-01

On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients

Sobre (1, 1) pares coherentes simétricos y polinomios ortogonales Sobolev: un algoritmo para calcular coeficientes de Fourier

DOI:

https://doi.org/10.15446/recolma.v53n2.85524

Palabras clave:

Orthogonal polynomials, Symmetric (1 1)-coherent pairs, Sobolev-Fourier series (en)
Polinomios ortogonales, Pares Simétricos (1 1)-Coherentes, Series Sobolev-Fourier (es)

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Autores/as

Herbert Dueñas Ruiz Universidad Nacional de Colombia
Francisco Marcellán Universidad Carlos III de Madrid and Instituto de Ciencias Matemáticas (ICMAT)
Alejandro Molano Universidad Pedagógica y Tecnológica de Colombia

Resumen (en)
Resumen (es)

In the pioneering paper [13], the concept of Coherent Pair was introduced by Iserles et al. In particular, an algorithm to compute Fourier Coefficients in expansions of Sobolev orthogonal polynomials defined from coherent pairs of measures supported on an infinite subset of the real line is described. In this paper we extend such an algorithm in the framework of the so called Symmetric (1, 1)-Coherent Pairs presented in [8].

En el artículo pionero [13], fue introducido el concepto de Par Coherente por Iserles et al. En particular, allí es descrito un algoritmo para calcular coeficientes de Fourier de expansiones de polinomios ortogonales de tipo Sobolev definidos a partir de pares de medidas coherentes soportadas en un subconjunto infinito de la recta real. En esta contribución extendemos tal algoritmo en el contexto de los llamados Pares Simétricos (1, 1)-Coherentes presentados en [8].

Referencias

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Cómo citar

APA

Dueñas Ruiz, H., Marcellán, F. y Molano, A. (2019). On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients. Revista Colombiana de Matemáticas, 53(2), 139–164. https://doi.org/10.15446/recolma.v53n2.85524

ACM

[1]

Dueñas Ruiz, H., Marcellán, F. y Molano, A. 2019. On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients. Revista Colombiana de Matemáticas. 53, 2 (jul. 2019), 139–164. DOI:https://doi.org/10.15446/recolma.v53n2.85524.

ACS

(1)

Dueñas Ruiz, H.; Marcellán, F.; Molano, A. On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients. rev.colomb.mat 2019, 53, 139-164.

ABNT

DUEÑAS RUIZ, H.; MARCELLÁN, F.; MOLANO, A. On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. 2, p. 139–164, 2019. DOI: 10.15446/recolma.v53n2.85524. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/85524. Acesso em: 22 ene. 2025.

Chicago

Dueñas Ruiz, Herbert, Francisco Marcellán, y Alejandro Molano. 2019. «On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients». Revista Colombiana De Matemáticas 53 (2):139-64. https://doi.org/10.15446/recolma.v53n2.85524.

Harvard

Dueñas Ruiz, H., Marcellán, F. y Molano, A. (2019) «On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients», Revista Colombiana de Matemáticas, 53(2), pp. 139–164. doi: 10.15446/recolma.v53n2.85524.

IEEE

[1]

H. Dueñas Ruiz, F. Marcellán, y A. Molano, «On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients», rev.colomb.mat, vol. 53, n.º 2, pp. 139–164, jul. 2019.

MLA

Dueñas Ruiz, H., F. Marcellán, y A. Molano. «On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients». Revista Colombiana de Matemáticas, vol. 53, n.º 2, julio de 2019, pp. 139-64, doi:10.15446/recolma.v53n2.85524.

Turabian

Dueñas Ruiz, Herbert, Francisco Marcellán, y Alejandro Molano. «On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients». Revista Colombiana de Matemáticas 53, no. 2 (julio 1, 2019): 139–164. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/85524.

Vancouver

1.

Dueñas Ruiz H, Marcellán F, Molano A. On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients. rev.colomb.mat [Internet]. 1 de julio de 2019 [citado 22 de enero de 2025];53(2):139-64. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/85524

Descargar cita

CrossRef Cited-by

4

1. Luis Alejandro Molano Molano. (2023). Inverse problems, Sobolev–Chebyshev polynomials and asymptotics. Ukrains’kyi Matematychnyi Zhurnal, 75(10), p.1411. https://doi.org/10.3842/umzh.v75i10.7293.

2. G. A. Marcato, F. Marcellán, A. Sri Ranga, Yen Chi Lun. (2023). Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case. Studies in Applied Mathematics, 151(2), p.475. https://doi.org/10.1111/sapm.12583.

3. M. Hancco Suni, G.A. Marcato, F. Marcellán, A. Sri Ranga. (2023). Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials. Journal of Mathematical Analysis and Applications, 525(1), p.127118. https://doi.org/10.1016/j.jmaa.2023.127118.

4. Luis Alejandro Molano Molano. (2024). Inverse Problems, Sobolev–Chebyshev Polynomials, and Asymptotics. Ukrainian Mathematical Journal, 75(10), p.1601. https://doi.org/10.1007/s11253-024-02281-3.