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Matematicheskie Zametki, 2010, Volume 87, Issue 3, Pages 443–452
DOI: https://doi.org/10.4213/mzm6593 (Mi mzm6593) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Fourier–Haar Coefficients and Properties of Continuous Functions

V. Tsagareishvili

Tbilisi Ivane Javakhishvili State University
Full-text PDF (433 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm6593
Abstract: 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)∈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, Fourier–Haar coefficient, continuous function, Abel transformation, binary irrational point.
Received: 24.10.2008
Revised: 07.07.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 3, Pages 416–424
DOI: https://doi.org/10.1134/S0001434610030132
Bibliographic databases:
Document Type: Article
UDC: 517.521
Language: Russian
Citation: V. Tsagareishvili, “Fourier–Haar Coefficients and Properties of Continuous Functions”, Mat. Zametki, 87:3 (2010), 443–452; Math. Notes, 87:3 (2010), 416–424
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm6593
  • https://www.mathnet.ru/eng/mzm/v87/i3/p443
    • This publication is cited in the following 1 articles:
    1. Alexander N. Shchitov, “The Exact Estimates of Fourier-Haar Coefficients of Functions of Bounded Variation”, IJARM, 4 (2016), 14  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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