A Fourier series (/ˈfʊrieɪ, -iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a...
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In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function...
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In mathematics, the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical...
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Poisson summation formula (category Fourier analysis)
that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently...
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Dirac delta function (category Fourier analysis)
measure theory or the theory of distributions. Joseph Fourier presented what is now called the Fourier integral theorem in his treatise Théorie analytique...
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Dini criterion (category Fourier series)
function f with |f(t)| ≤ g(t) whose Fourier series does not converge at 0. Dini, Ulisse (1880), Serie di Fourier e altre rappresentazioni analitiche delle...
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Informally, if the Fourier transform of a function f {\displaystyle f} vanishes on a certain set Z {\displaystyle Z} , the Fourier transform of any linear...
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Carleson's theorem (category Theorems in Fourier analysis)
establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of L2 functions, proved by Lennart Carleson (1966). The name is...
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Dini–Lipschitz criterion (category Fourier series)
respect to δ {\displaystyle \delta } . Dini, Ulisse (1872), Sopra la serie di Fourier, Pisa Golubov, B. I. (2001) [1994], "Dini-Lipschitz criterion", Encyclopedia...
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(Gauthier-Villars, 1866) Jordan, Camille (1881). "Sur la série de Fourier" [On the Fourier series]. Comptes rendus hebdomadaires des séances de l'Académie...
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Laurent series (redirect from Laurent serie)
{\displaystyle r<\varrho <R} , this just amounts to computing the complex Fourier coefficients of the restriction of f {\displaystyle f} to γ {\displaystyle...
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Torsten Carleman, he can be viewed as a moderate modernizer of classical Fourier analysis. Shmuel Agmon, Jean-Pierre Kahane, Yitzhak Katznelson, Paul Malliavin...
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Wiener algebra (category Fourier series)
Wiener and usually denoted by A(T), is the space of absolutely convergent Fourier series. Here T denotes the circle group. The norm of a function f ∈ A(T)...
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Olivier Giroud (category Serie A players)
and techniques of physical and sports activities (STAPS) at the Joseph Fourier University, in Grenoble. Giroud began organised football playing for his...
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les coefficients de Fourier des formes modulaires de poids demi-entier", Journal de Mathématiques Pures et Appliquées, Neuvième Série, 60 (4): 375–484,...
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ISBN 978-0-7167-4106-0. Kolmogorov, A. (1923). "Une série de Fourier–Lebesgue divergente presque partout" [A Fourier–Lebesgue series that diverges almost everywhere]...
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to define powers, including fractional ones, of the Fourier transform, to wit a Fractional Fourier transform generalization, in effect a Mehler kernel...
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Marcinkiewicz interpolation theorem (category Fourier analysis)
computed by first taking the Fourier transform of f, then multiplying by the sign function, and finally applying the inverse Fourier transform. Hence Parseval's...
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Friedel's law (category Fourier analysis)
Friedel, is a property of Fourier transforms of real functions. Given a real function f ( x ) {\displaystyle f(x)} , its Fourier transform F ( k ) = ∫ −...
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mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in...
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confused with Dini's theorem. One of his students was Luigi Bianchi. Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile...
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arithmetic operations and thus reduced bit complexity. Combining this with fast Fourier transform-based methods of multiplying integers makes computing the digits...
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interferometers are now used to capture speckled images, which are synthesized using Fourier analysis to produce a portrait of high resolution. It was this methodology...
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branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is...
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trigonométrique. Quatrieme Partie. Les totalisations. Solution du probléme de Fourier. Premier Fascicule: Les totalisations. Deuxième Fascicule: Appendices et...
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(1977). "Sur les coefficients de Fourier des fonctions continues". Comptes Rendus de l'Académie des Sciences, Série A et B. 285 (16): A1001–A1003. ISSN 0997-4482...
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Encyclopedia of Mathematics, EMS Press Jordan, Camille (1881), "Sur la série de Fourier", Comptes rendus hebdomadaires des séances de l'Académie des sciences...
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and writer. Jean-François Champollion (1790–1832) – Egyptologist. Joseph Fourier (1768–1830) – mathematician and physicist. Louis Néel (1904–2000) – physicist...
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quantities Active DIN 5486 Notation of matrices Withdrawn DIN 1303 DIN 5487 Fourier-, Laplace- and Z-transformation; symbols and concepts Active DIN 5489 Directions...
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G (1987). "Sur une question de V. A. Lebesgue". Annales de l'Institut Fourier. 37 (3): 19–37. doi:10.5802/aif.1096. Ribenboim, pp. 57–63 Mordell 1921...
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