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On sequences of Fourier coefficients of functions of Hölder classes

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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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    V. S. Mityagin, “On absolute convergence of series of Fourier coefficients,” Dokl. Akad. Nauk SSSR,157, No. 5, 1047–1050 (1964).

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