scholarly journals Convergence of Multiple Fourier Series of Functions of Bounded Generalized Variation

2015 ◽  
Vol 67 (2) ◽  
pp. 186-198
Author(s):  
U. Goginava ◽  
A. Sahakian
Keyword(s):  
Fourier Series ◽  
Multiple Fourier Series ◽  
Generalized Variation ◽  
Series Of Functions

Absolute convergence of multiple Fourier series of a function of p(n)-Λ-BV

2018 ◽  
Vol 25 (3) ◽  
pp. 481-491
Author(s):  
Rajendra G. Vyas
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Multiple Fourier Series ◽  
Series Of Functions ◽  
Sufficiency Conditions

AbstractIn this paper, we obtain sufficiency conditions for generalized β-absolute convergence ({0<\beta\leq 2}) of single and multiple Fourier series of functions of the class {\Lambda\text{-}\mathrm{BV}(p(n)\uparrow\infty,\varphi,[-\pi,\pi])} and the class {(\Lambda^{1},\Lambda^{2},\dots,\Lambda^{N})\text{-}\mathrm{BV}(p(n)\uparrow% \infty,\varphi,[-\pi,\pi]^{N})}, respectively.

Some properties of an odd-dimensional space

2020 ◽  
Vol 27 (2) ◽  
pp. 321-330
Author(s):  
Vakhtang Tsagareishvili
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Dimensional Space ◽  
Multiple Fourier Series ◽  
Partial Derivatives ◽  
Several Variables ◽  
The Absolute ◽  
Series Of Functions ◽  
Russian Math

AbstractIn this paper, we investigate the absolute convergence of Fourier series of functions in several variables for an odd-dimensional space when these functions have continuous partial derivatives. It should be noted that similar properties for an even-dimensional space were given in [L. D. Gogoladze and V. S. Tsagareishvili, On absolute convergence of multiple Fourier series (in Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 2015, 9, 12–21; translation in Russian Math. (Iz. VUZ) 59 (2015), no. 9, 9–17]. The obtained results are the best possible in a certain sense.

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