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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.22 n.1 San José Jan./Jun. 2015


Cálculo de coeficientes de fourier en dos variables, una versión distribucional

Fourier coefficientes computation in two variables, a distributional version

Carlos Manuel Ulate R.*+


En el presente artículo, a partir de la fórmula distribucional de sumación del tipo de Euler-Maclaurin y una adecuada elección de la distribución, se obtienen representaciones para los coeficientes de Fourier en dos variables. Estas representaciones pueden ser usadas para la evaluación numérica de los coeficientes.

Palabras clave: Sumas Euler-Maclaurin; coeficientes de Fourier; distribuciones.


The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in representations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.

Keywords: Euler-Maclaurin sums, Fourier coefficients, distributions.

Mathematics Subject Classification: 40G05, 42A16.

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[1] Estrada, R.; Kanwal R.P. (1994) Asymptotic Analysis: A Distributional Approach. Birkhäuser, Boston.         [ Links ]

[2] Kanwal, R.P. (1997) Generalized Functions: Theory and Technique, 2a edición. Birkhäuser, Boston.         [ Links ]

[3] Lyness, J. N. (1970) “The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula, Part I. Functions whose early derivatives are continuous”, Math. of Comp. 24: 101–135.         [ Links ]

[4] Schwartz, L. (1966) Théorie des Distributions. Hermann, Paris.         [ Links ]

[5] Ulate, C.M.; Estrada, R. (1998) “Una fórmula distribucional de sumación del tipo de Euler-Maclaurin en dos variables”, Divulgaciones Matemáticas 6: 93–112.         [ Links ]

* Sede de Occidente, Universidad de Costa Rica, San Ramón, Costa Rica. E-Mail:

Received: 15/Feb/2012; Revised: 3/Sep/2014;Accepted: 17/Oct/2014

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