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- W1990853911 abstract "their arithmetic means. It is a classical result of the theory of Fejer and Lebesgue that the sequence {-In (x) } is uniformly bounded and satisfies (1.5) |0-n(x) I < and that, as n -oo, ofn(x)-*f(x) uniformly over (-7r, 7r) provided f(x) is continuous in (-7r, ir). As to the partial sums (1.3) themselves, as may be shown by suitable examples, they need not be uniformly bounded even when (1.1) is satisfied, and the sequence {Sn(x) } need not converge uniformly to f(x) even whenf(x) is continuous in (-7r, 7r). Under these circumstances special attention should be given to a recent result of Paleyt according to which the non-negativeness of the Fourier coeffi-" @default.
- W1990853911 created "2016-06-24" @default.
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- W1990853911 date "1935-02-01" @default.
- W1990853911 modified "2023-09-27" @default.
- W1990853911 title "Some generalizations of Paley’s theorems on Fourier series with positive coefficients" @default.
- W1990853911 doi "https://doi.org/10.1090/s0002-9947-1935-1501810-4" @default.
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