On the Uniform Summability of Multiple Walsh-Fourier Series |
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Authors: | U Goginava |
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Institution: | (1) Department of Mechanics and Mathematics, Tbilisi State University, University St. 2, Tbilisi, 380 043, Georgia |
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Abstract: | In this paper we prove that if f C
( 0, 1
N
) and the function f is of bounded partial variation, then the N-dimensional Walsh-Fourier series of the function f is uniformly (C,– ) summable ( 1 +...+
N
< 1,
i
> 0, i = 1,...,N) in the sense of Pringsheim. If 1 +...+
N
= 1,
i
> 0, i = 1,2,...,N, then there exists a continuous function f
0 of bounded partial variation on 0, 1]
N
such that the Cesàro (C,– ) means
m
–
(f0,Õ) of the N-dimensional Walsh-Fourier series of f
0 diverge over cubes. |
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Keywords: | |
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