On Fluctuating Functionsappeared in the Transactions of the Royal Irish Academy, volume 19 (1843), pp. 264-321.
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In this paper, Hamilton sets out to explain the validity of the Fourier inversion formula by means of a principle which he calls the Principle of Fluctuation. He also uses this principle to obtain generalizations of the Fourier Inversion Formula. He also considers the representation of periodic functions by Fourier series, and discusses various applications of Fourier analysis.
An abstract of Hamilton's paper On Fluctuating Functions was published in volume 1 of the Proceedings of the Royal Irish Academy (1841), pp. 475-477.
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