scholarly journals A note on the strong summability of two-dimensional Walsh–Fourier series

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
George Tephnadze
Keyword(s):  
Fourier Series ◽  
Strong Convergence ◽  
Studia Math ◽  
Trigonometric Fourier Series ◽  
Strong Summability ◽  
Two Dimensional ◽  
Convergence Theorems ◽  
Two Parameter

AbstractIn this paper, we investigate the strong summability of two-dimensional Walsh–Fourier series obtained in [F. Weisz, Strong convergence theorems for two-parameter Walsh–Fourier and trigonometric-Fourier series, Studia Math. 117 1996, 2, 173–194] (see Theorem W) and prove the sharpness of this result.

scholarly journals Strong convergence of two-dimensional Vilenkin-Fourier series

2015 ◽  
Vol 289 (4) ◽  
pp. 485-500
Author(s):  
Nacima Memić ◽  
Ilona Simon ◽  
George Tephnadze
Keyword(s):  
Fourier Series ◽  
Strong Convergence ◽  
Two Dimensional

A note on strong summability of two-dimensional Walsh-Fourier series

2013 ◽  
Vol 66 (2) ◽  
pp. 211-219
Author(s):  
Ushangi Goginava ◽  
Larry Gogoladze
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Two Dimensional

On the Exponential Uniform Strong Summability of Multiple Trigonometric Fourier Series

2009 ◽  
Vol 16 (3) ◽  
pp. 517-532
Author(s):  
Larry Gogoladze
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series ◽  
Strong Summability ◽  
Multiple Trigonometric Fourier Series

Abstract In the paper, in particular, it is proved that the 𝑠-dimensional trigonometric Fourier series of the 2π-periodic continuous on [–π, π]𝑠 function 𝑓 is uniformly strong summable to the function 𝑓 exponentially in the power . Moreover, it is proved that this result is best possible.

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