The Fourier Series: A Historical Perspective

Authors

  • Alejandro Ortiz Fernández Pontificia Universidad Católica del Perú, Sección Matemáticas. Perú

DOI:

https://doi.org/10.17268/sel.mat.2018.01.11

Keywords:

Trigonometric Fourier, Trigonometric Series, String Vibration, Dirichlet, Lebesgue, Distributions

Abstract

The ain of this paper is present a vision of an essential field of the modern analysis like it is the Fourier analysis. we focus on some historical aspects and then we explain the analytical arguments that are accessible to understand.
We think this subject is not very well know in Peru, our country, especially inthe way we address this subject. By the other hand, this text is about the classical aspects of the Fourier theory.

References

Avila, G. Evolucao dos Conceitos de Funcao e Integral. Matemática Universitaria. N-1. 1985.

Carslaw, H.S. Introduction to the theory of Fourier’s Series and Integrals. Dover. Pub. 1930.

Figueiredo, D. Análise de Fourier e Equacoes Diferenciais Parciais. Projeto Euclides. 1977.

Gasquet, C.; Witomski, P. Analyse de Fourier et Applications. Masson. Paris. 1990.

Horvath, J. Desarrollo del Análisis Funcional. México. 1972.

Jeffery, R.L. Trigonometric Series. Univ. of Toronto Press. 1956.

Kestelman, H. Modern Theories of Integration. Dover. Pub. 1960.

Myint, U.T. Partial Differential Equations of Mathematical Physics. Amer. Elsevier Pub. Corp. 1973.

Ortiz, A. Integrales Singulares y Temas Afines Pro-Matemática. PUCP. 1991.

Ortiz, A. La Matemática a Través de Clásicas Áreas. Vol. 3 PUCP. UNT. Lima Febrero. 2017.

Zygmund, A. Trigonometric Series. Cambridge. 1968.

Torchinsky, A. Real-Variable Methods in Harmonic Analysis. Acad. Press. USA. 1986.

Schwartz, L. Théorie des Distributions. Hermann. París. 1966.

Published

2018-07-27

How to Cite

Ortiz Fernández, A. (2018). The Fourier Series: A Historical Perspective. Selecciones Matemáticas, 5(01), 102 - 120. https://doi.org/10.17268/sel.mat.2018.01.11

Issue

Section

Mathematics' Teaching

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