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- Fejér's_theorem abstract "In mathematics, Fejér's theorem, named for Hungarian mathematician Lipót Fejér, states that if f:R → C is a continuous function with period 2π, then the sequence (σn) of Cesàro means of the sequence (sn) of partial sums of the Fourier series of f converges uniformly to f on [-π,π].Explicitly,whereandwith Fn being the nth order Fejér kernel.A more general form of the theorem applies to functions which are not necessarily continuous (Zygmund 1968, Theorem III.3.4). Suppose that f is in L1(-π,π). If the left and right limits f(x0±0) of f(x) exist at x0, or if both limits are infinite of the same sign, thenExistence or divergence to infinity of the Cesàro mean is also implied. By a theorem of Marcel Riesz, Fejér's theorem holds precisely as stated if the (C, 1) mean σn is replaced with (C, α) mean of the Fourier series (Zygmund 1968, Theorem III.5.1).".
- Fejér's_theorem wikiPageID "5135754".
- Fejér's_theorem wikiPageRevisionID "569367053".
- Fejér's_theorem subject Category:Fourier_series.
- Fejér's_theorem subject Category:Theorems_in_approximation_theory.
- Fejér's_theorem comment "In mathematics, Fejér's theorem, named for Hungarian mathematician Lipót Fejér, states that if f:R → C is a continuous function with period 2π, then the sequence (σn) of Cesàro means of the sequence (sn) of partial sums of the Fourier series of f converges uniformly to f on [-π,π].Explicitly,whereandwith Fn being the nth order Fejér kernel.A more general form of the theorem applies to functions which are not necessarily continuous (Zygmund 1968, Theorem III.3.4). Suppose that f is in L1(-π,π).".
- Fejér's_theorem label "Fejér's theorem".
- Fejér's_theorem label "Satz von Fejér".
- Fejér's_theorem label "Théorème de Fejér".
- Fejér's_theorem label "Twierdzenie Fejéra".
- Fejér's_theorem sameAs Fej%C3%A9r's_theorem.
- Fejér's_theorem sameAs Satz_von_Fejér.
- Fejér's_theorem sameAs Théorème_de_Fejér.
- Fejér's_theorem sameAs フェイェールの定理.
- Fejér's_theorem sameAs Twierdzenie_Fejéra.
- Fejér's_theorem sameAs Q571154.
- Fejér's_theorem sameAs Q571154.
- Fejér's_theorem wasDerivedFrom Fejér's_theorem?oldid=569367053.