On the absolute convergence of Fourier series with respect to general orthonormal systems

2017 ◽  
Vol 24 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Vakhtang Tsagareishvili
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Multiple Fourier Series ◽  
Haar Series ◽  
The Absolute

AbstractThe problems of absolute convergence of multiple Fourier series with respect to both general orthonormal systems and multiple Haar series are studied.

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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