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Named after French mathematician and physicistJoseph Fourier (1768-1830), who pioneered research into such series and their application to problems of heat transfer and vibration.
1951 , R. C. H. Young (translator), Konrad Knopp, Theory and Application of Infinite Series, , 1990, Dover, Unabridged unaltered reprint of 2nd English Edition, page 493,
As we have seen (pp. 369—370), the question of the necessary and sufficient conditions under which the Fourier series of an integrable function converges and represents the given function is one which presents very great difficulties.
There are excellent discussions of Fourier series and integrals in Katznelson and Dym and McKean . The book by R. E. Edwards is an exhaustive study of Fourier series from a more modern perspective.
2006, K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd edition, Cambridge University Press, page 415:
Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.
Fourier analysis on Wikipedia.Wikipedia 