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On sequences of Fourier coefficients of functions of Hölder classes

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Abstract

The following theorem is proved. Let {ψ k(t)} be an arbitrary complete orthonormal system on [0, 1] and let 1/2<α<1. Then anf(t)∈ Cβ exists for allβ<α such that ∑ k=1 · |ck(f)|p=∞, p=2/(l+2α), where\(c_k \left( f \right) = \int\limits_1^0 {f\psi _k dt} \).

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Literature cited

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Additional information

Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 567–572, November, 1969.

The authors wish to thank P. P. Zabreiko and P. L. Ul'yanov for helpful discussions and remarks.

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Abros'kina, G.S., Mityagin, B.S. On sequences of Fourier coefficients of functions of Hölder classes. Mathematical Notes of the Academy of Sciences of the USSR 6, 800–803 (1969). https://doi.org/10.1007/BF01101407

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Keywords

  • Fourier
  • Fourier Coefficient
  • Orthonormal System
  • Complete Orthonormal System
  • Arbitrary Complete Orthonormal System