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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 no.2 Bogotá July/Dec. 2019 Epub Mar 20, 2020
Artículos originales
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
1 Departamento de Matemáticas Universidad Nacional de Colombia Ciudad Universitaria Bogotá, Colombia e-mail: haduenasr@unal.edu.co
2 Departamento de Matemáticas Universidad Carlos III de Madrid Avenida de la Universidad 30, 28911 Legan Es, Spain e-mail: pacomarc@ing.uc3m.es
3 Escuela de Matemáticas y Estadística Universidad Pedagógica y Tecnológica de Colombia Escuela de Matemáticas y Estadística Carrera 18-22, 150461 Duitama, Colombia e-mail: luis.molano01@uptc.edu.co
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].
Key words and phrases. Orthogonal polynomials; Symmetric (1,1)-coherent pairs; Sobolev-Fourier series
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].
Palabras y frases clave. Polinomios ortogonales; Pares Simetricos (1, 1) -Coherentes; Series Sobolev-Fourier
Acknowledgements.
The authors thank the referees for the careful revision of the manuscript. Their suggestions and criticisms have contributed to improving the presentation. The work by Francisco Marcellán has been supported by Agencia Estatal de Investigación of Spain, grant PGC2018-096504-B-C33. The work by Alejandro Molano has been partially supported by Dirección de Investigaciones, Universidad Pedagógica y Tecnológica de Colombia, research project code 1922.
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Received: February 2019; Accepted: July 2019
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