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Matematicheskie Zametki, 2012, Volume 91, Issue 5, Pages 691–703
DOI: https://doi.org/10.4213/mzm9358 (Mi mzm9358) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Fourier Coefficients of Continuous Functions

L. Gogoladze, V. Tsagareishvili

Tbilisi Ivane Javakhishvili State University
Full-text PDF (449 kB) Citations (18)
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DOI: https://doi.org/10.4213/mzm9358
Abstract: It is well known that the Fourier coefficients of continuous functions with respect to classical orthogonal systems (trigonometric, Haar, and Walsh) can be estimated via the moduli of continuity of the functions. However, not all orthonormal systems possess this property. We obtain necessary and sufficient conditions on orthonormal systems such that the Fourier coefficients of continuous functions with respect to these orthonormal systems can be estimated via the moduli of continuity in a certain sense.
Keywords: orthonormal system, continuous function, Fourier coefficients, modulus of continuity, Haar system, Hölder's inequality, Abel transform.
Received: 27.12.2010
Revised: 17.02.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 5, Pages 645–656
DOI: https://doi.org/10.1134/S0001434612050057
Bibliographic databases:
Document Type: Article
UDC: 517.521
Language: Russian
Citation: L. Gogoladze, V. Tsagareishvili, “Fourier Coefficients of Continuous Functions”, Mat. Zametki, 91:5 (2012), 691–703; Math. Notes, 91:5 (2012), 645–656
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
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