Abstract
Fourier series decompose periodic functions or periodic signals into the sum of a countable family of simple oscillating functions, namely sines and cosines (or complex exponentials).
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Carleson, L.: On the convergence and growth of partial sums of Fourier series. Acta Math. 116, 135–157 (1966)
Bhatia, R.: Notes on Functional Analysis. Hindustan Book Agency, New Delhi (2009)
Vladimirov, V.S.: Equations of Mathematical Physics. Marcel Dekker, New York (1971)
Gonzalez-Velasco, E.A.: Connections in mathematical analysis: the case of Fourier series. Am. Math. Mon. 99(5), 427–441 (1992)
Zygmund, A.: Trigonometric Series, 2nd edn. Cambridge University Press, Cambridge (1988)
Boas, R.P.: Summation formulas and band-limited signals. Tohoku Math. J. 24, 121–125 (1972)
Steiner, A.: Plancherel’s theorem and the Shannon series derived simultaneously. Am. Math. Mon. 87, 193–197 (1980)
Higgins, J.R.: Five short stories about the cardinal series. Bull. Am. Math. Soc. 12, 45–89 (1985)
Bhatia, R.: Fourier Series. The Mathematical Association of America, Washington (2005)
Grafakos, L.: Classical Fourier Analysis, 2nd edn. Springer, New York (2008)
Grafakos, L.: Modern Fourier Analysis, 2nd edn. Springer, New York (2009)
Kaiser, G.: A Friendly Guide to Wavelets. Birkhäuser, Boston (1994)
Chernoff, P.R.: Pointwise convergence of Fourier series. Am. Math. Mon. 87, 399–400 (1980)
Jordan, C.: Sur la série de Fourier. C.R. Acad. Sci. Paris, 92, 228–230 (1881)
Lebesgue, H.: Leçons sur les séries trigonométriques. Gauthier-Villars, Paris (1906)
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Choudary, A.D.R., Niculescu, C.P. (2014). Fourier Series. In: Real Analysis on Intervals. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2148-7_12
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DOI: https://doi.org/10.1007/978-81-322-2148-7_12
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