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This article is cited in 7 scientific papers (total in 7 papers)
Differentiable functions and general orthonormal systems
Larry Gogoladze, Vakhtang Tsagareishvili I. Javakhishvili Tbilisi State University, 13 University Str., Tbilisi 0186, Georgia
Abstract:
The properties of the Fourier series of the functions from some differentiable class are well known for classical orthonormal systems (trigonometric, Haar, Walsh, etc.). On the other hand, S. Banach proved that good differential properties of a function do not guarantee the a.e. convergence of the Fourier series of this function with respect to general orthonormal systems (ONS). Therefore, in order to obtain well-known results for general ONS, we need to impose specific conditions on the given system. In the present paper we find conditions on the functions of an ONS under which the Fourier series of differentiable functions are convergent a.e.
Key words and phrases:
Orthonormal system, Fourier coefficients, bounded variation.
Citation:
Larry Gogoladze, Vakhtang Tsagareishvili, “Differentiable functions and general orthonormal systems”, Mosc. Math. J., 19:4 (2019), 695–707
Linking options:
https://www.mathnet.ru/eng/mmj750 https://www.mathnet.ru/eng/mmj/v19/i4/p695
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