The inauguration of trigonometric series in Fourier's \textit{Théorie analytique de la chaleur} and in the vibrating strings controversy
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Publication:2875818
zbMATH Open1304.01024arXiv1211.0794MaRDI QIDQ2875818
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Publication date: 12 August 2014
Published in: (Search for Journal in Brave)
Abstract: Cet article applique les notions de texte et denonc'e inaugural `a la Th'eorie analytique de la chaleur de Fourier et `a la controverse des cordes vibrantes. Il 'etablit que seul le livre de Fourier est un texte inaugural. Il propose en outre une analyse s'emiotique des modes d'expression de la g'en'eralit'e qui permet dans chaque cas de clarifier les conditions d'introduction de la possibilit'e de repr'esenter une fonction arbitraire par des s'eries trigonom'etriques. (The inauguration of trigonometrical series in Fourier's Th'eorie analytique de la chaleur and in the vibrating strings controversy) This paper applies the notions of inaugural text and statement to Fourier's Th'eorie analytique de la chaleur and to the vibrating strings controversy. It establishes that only Fourier's book is an inaugural text. It presents also a semiotic analysis of the expression modes of generality which allows to clarify in both cases the conditions of introducing of the possibility to represent an arbitrary function by trigonometrical series.
Full work available at URL: https://arxiv.org/abs/1211.0794
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