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Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity

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Abstract

It is proved that a quasiconvex sequenceλ v of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuityω(gd) into uniformly convergent series if and only ifλ n ω(1/n) log n → 0 for n →∞. The sufficiency of this condition is already known.

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Literature cited

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Translated from Matematicheskie Zametki, Vol. 8, No. 5,pp. 619–623, November, 1970.

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Telyakovskii, S.A. Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity. Mathematical Notes of the Academy of Sciences of the USSR 8, 817–819 (1970). https://doi.org/10.1007/BF01146938

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Keywords

  • Fourier
  • Fourier Series
  • Convergent Series
  • Convergence Factor