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Artículos

Vol. 3 No. 3 (2000): Noviembre

UNA PERSPECTIVA HISTÓRICA DE LAS SERIES DE FOURIER: DE LAS ECUACIONES DE ONDAS Y DEL CALOR A LOS OPERADORES COMPACTOS Y AUTOADJUNTOS

Submitted
March 16, 2025
Published
2000-11-30

Abstract

One of the problems worked on by eighteenth century mathematicians is the "vibrant cord problem". This was studied by D'Alembert, Euler and shortly after in 1753, by Daniel Ber-noulli. The solution provided by the last consisted in expressing it as a superposition of simple waves. His ideas were applied and improved by Fourier in 1807 in the study of heat conduc-tion. They were written in the work "Théorie analytique de la Chaleur" published in 1822. Reasoning by Fourier exposed controversies and questions that have influenced the history of Mathematics. Here we comment some of them, such as the existence of continuous non-derived functions, Cantor's compound theory and notions of the integral by Cauchy, Riemann and Lebesgue. We also handled the current presentation of the series by Fourier. Finally, we commented on the role played in this century by Functional Analysis in placing Fourier's series within its abstract framework.

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