Approximation by Nörlund means of Walsh-Fourier series
نویسندگان
چکیده
منابع مشابه
Approximation by Nörlund Means of Double Walsh–fourier Series for Lipschitz Functions
For double trigonometric Fourier series, Móricz and Rhoades studied the rate of uniform approximation by Nörlund means of the rectangular partial sums of double Fourier series of a function belonging to the class Lipα (0 < α 1) [12] and the class of continuous functions [13], on the two-dimensional torus. As a special case, they obtained the rate of uniform approximation by double Cesàro means....
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Every function f(x) which is of period 1 and Lebesgue integrable on [0, 1 ] may be expanded in a Walsh-Fourier series(3), f(x)~ ?.?=n ak\pk(x), where ak=fof(x)ypk(x)dx, k=0, 1, 2, • • • . Fine exhibited some of the basic similarities and differences between the trigonometric orthonormal system and the Walsh system. He identified the Walsh functions with the full set of characters of the dyadic ...
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A many of approximation methods in C2 (Fej er, de la Vall ee Poussin etc.) may be generated via a certain function ' 2 C[0;1] with '(0) = 1, '(1) = 0. The function 'j(t) = cos(j 1=2) t (j 2 N) generates the Rogosinski approximation method [N. K. Bari, "A Treatise on Trigonometric Series," I, II, Pergamon Press, 1964]. Our idea consists in representing ' by the orthogonal system 'j to extend res...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1992
ISSN: 0021-9045
DOI: 10.1016/0021-9045(92)90067-x