Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system

1968 ◽  
Vol 4 (2) ◽  
pp. 618-623
Author(s):  
S. V. Bochkarev
Keyword(s):  
Fourier Series ◽  
Haar System ◽  
Continuous Functions ◽  
Unconditional Convergence ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere

On the constancy of signs and order of magnitude of Fourier–Haar coefficients

2018 ◽  
Vol 25 (3) ◽  
pp. 357-361
Author(s):  
Larry Gogoladze ◽  
Vakhtang Tsagareishvili
Keyword(s):  
Fourier Series ◽  
Haar System ◽  
Nauk Sssr ◽  
Continuous Functions ◽  
Nonincreasing Function ◽  
Akad Nauk Sssr ◽  
Order Of Magnitude

AbstractIn the paper, we investigate the relation between the properties of functions and their Fourier–Haar coefficients. We show that for some classes of functions Fourier–Haar coefficients have constant signs and order of magnitude. In 1964, Golubov proved in [B. I. Golubov, On Fourier series of continuous functions with respect to a Haar system (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 28 1964, 1271–1296] that if {f(x)\in C(0,1)}, then its Fourier–Haar coefficients have constant signs when {f(x)} is a nonincreasing function on {[0,1]}, and in some cases those coefficients have a certain order of magnitude. In the present paper, we continue to investigate the properties of functions which follow from the behavior of their Fourier–Haar coefficients.

scholarly journals Convergence almost everywhere of multiple Fourier series over cubes

2017 ◽  
Vol 370 (3) ◽  
pp. 1629-1659
Author(s):  
Mieczysław Mastyło ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Fourier Series ◽  
Multiple Fourier Series ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere
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