Absolute convergence of Fourier series of functions of λBV(p) and ϕλBV

1982 ◽  
Vol 40 (3-4) ◽  
pp. 273-276 ◽  
Author(s):  
M. Schramm ◽  
D. Waterman
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
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.

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.

Absolute convergence factors of Lipschitz class functions for general Fourier series

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vakhtang Tsagareishvili ◽  
Giorgi Tutberidze
Keyword(s):  
Fourier Series ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Orthonormal System ◽  
Lipschitz Class ◽  
Series Of Functions

Abstract The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions f ∈ Lip ⁡ 1 {f\in\operatorname{Lip}1} class provides absolute convergence of Fourier series. In particular, we found special conditions for the functions of orthonormal system (ONS), for which the above sequences are absolute convergence factors of Fourier series of functions of Lip ⁡ 1 {\operatorname{Lip}1} class. It is established that the resulting conditions are best possible in certain sense.

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.

A SUMMABILITY METHOD FOR FOURIER SERIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION

Analysis ◽  
1997 ◽  
Vol 17 (2-3) ◽  
pp. 287-300
Author(s):  
LAWRENCE A. D'ANTONIO ◽  
DANIEL WATERMAN
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Summability Method ◽  
Series Of Functions
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