Geodesic
Fourier--Haar Coefficients and Properties of Continuous Functions
Matematičeskie zametki, Tome 87 (2010) no. 3, pp. 443-452

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It is well known that if the Fourier–Haar coefficients have a certain order or if a certain series composed of the Fourier–Haar coefficients of a function $f(x)\in C(0,1)$ converges, then the function has a certain form. In the present paper, we prove that not only the Fourier–Haar coefficients, but also the difference of these coefficients possess these properties.
Keywords: orthonormal Haar system, continuous function, binary irrational point.
Mots-clés : Fourier–Haar coefficient, Abel transformation 
@article{MZM_2010_87_3_a11,
     author = {V. Tsagareishvili},
     title = {Fourier--Haar {Coefficients} and {Properties} of {Continuous} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {443--452},
     publisher = {mathdoc},
     volume = {87},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_3_a11/}
}
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V. Tsagareishvili. Fourier--Haar Coefficients and Properties of Continuous Functions. Matematičeskie zametki, Tome 87 (2010) no. 3, pp. 443-452. http://geodesic.mathdoc.fr/item/MZM_2010_87_3_a11/