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.

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.

Operator ideals and the absolute convergence of Fourier series

2011 ◽  
Vol 48 (1) ◽  
pp. 104-115
Author(s):  
Manuel Fugarolas
Keyword(s):  
Fourier Series ◽  
Besov Spaces ◽  
Absolute Convergence ◽  
Operator Ideals ◽  
Entropy Numbers ◽  
Approximation Numbers ◽  
Convergent Fourier Series ◽  
The Absolute ◽  
Series Of Functions

In this paper we give some relationships between the absolutely convergent Fourier series of functions belonging to Besov spaces and their connection with the theory of operator ideals. In this context, we give results in operator ideals associated with generalized approximation numbers, Weyl numbers and entropy numbers.

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.

On the Absolute Convergence of Fourier Series of Functions of ∧𝐵𝑉(𝑝) and φ ∧𝐵𝑉

2007 ◽  
Vol 14 (4) ◽  
pp. 769-774
Author(s):  
Rajendra G. Vyas
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Classical Result ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Natural Numbers ◽  
The Absolute ◽  
Series Of Functions ◽  
Sufficiency Conditions

Abstract Let 𝑓 be a 2π periodic function in 𝐿1[0,2π] and , be its Fourier coefficients. Extending the classical result of Zygmund, Schramm and Waterman obtained the sufficiency conditions for the absolute convergence of Fourier series of functions of ∧𝐵𝑉(𝑝) and φ ∧𝐵𝑉. Here we have generalized these results by obtaining certain sufficiency conditions for the convergence of the series , where is a strictly increasing sequence of natural numbers and 𝑛–𝑘 = –𝑛𝑘 for all 𝑘, for such functions.

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