Abstract
It is proved that a sequence of factors {λ v }, which are Fourier-Stieitjes coefficients, converts the Fourier series of any function whose modulus of continuity does not exceed a given modulus of continuity ω(δ) into a uniformly convergent series, if and only if
The Sufficiency of this condition is known.
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Translated from Matematicheskii Zametki, Vol. 10, No. 1, pp. 33–40, July, 1971.
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Telyakovskii, S.A. Uniform-convergence factors for Fourier series of functions with a given modulus of continuity. Mathematical Notes of the Academy of Sciences of the USSR 10, 444–448 (1971). https://doi.org/10.1007/BF01747067
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DOI: https://doi.org/10.1007/BF01747067