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Does anyone know a good book or article on the History of the Fourier transform? It's first appearance (of the transform) and use in particular? Or at least some source with some historical information on that matter.

There is plenty about the Fourier series but I couldn't find much illuminating about the transform yet.

Thanks.

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My feeling about this is that the Fourier transform is a continuous version of the series. I therefore think that their history is somewhat tied together. – Spice the Bird Aug 5 '12 at 19:03
up vote 4 down vote accepted

I. Grattan Guinness, Joseph Fourier 1768-1830. A survey of his life and work, based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807.

Fourier transform, unlike Fourier series, was really invented by Fourier, when he studied the heat equation.

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