On the multipliers of Fourier series with respect to the Haar system

V. G. Krotov

doi:10.1007/bf02297691

On the multipliers of Fourier series with respect to the Haar system

Analysis Mathematica ◽

10.1007/bf02297691 ◽

1977 ◽

Vol 3 (3) ◽

pp. 187-198 ◽

Cited By ~ 1

Author(s):

V. G. Krotov

Keyword(s):

Fourier Series ◽

Haar System

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On the divergence of Fourier series in the general Haar system

Armenian Journal of Mathematics ◽

10.52737/18291163-2021.13.6-1-10 ◽

2021 ◽

pp. 1-10

Author(s):

Martin Grigoryan ◽

Artavazd Maranjyan

Keyword(s):

Fourier Series ◽

Measurable Function ◽

Haar System ◽

Bounded Measurable Function

For any countable set $D \subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]\backslash D$.

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

Georgian Mathematical Journal ◽

10.1515/gmj-2018-0034 ◽

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.

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