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Fourier coefficients of functions from the classesb andc. Parseval equality for the classc or for the Fourier-Stieltjes series

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Ukrainian Mathematical Journal Aims and scope

Abstract

We study restrictions that should be imposed on the numbers sequences {αn} and {Βn} in order to guarantee that the series\(\sum\nolimits_{n = 1}^\infty {a_n } \) cosnx and\(\sum\nolimits_{n = 1}^\infty {b_n } \) sinnx do not belong to the classesB orC for any {a n } and {b n } such thata n ≥α n ,b n ≥Β n ,n=1, 2,⊎.

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References

  1. A. Zygmund,Trigonometric Series, Vol. 1, Cambridge University Press, Cambridge (1959).

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Authors and Affiliations

  1. Moscow Institute of Physics and Engineering, Moscow

    A. A. Konyushkov

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  1. A. A. Konyushkov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1455–1460, October, 1993.

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Konyushkov, A.A. Fourier coefficients of functions from the classesb andc. Parseval equality for the classc or for the Fourier-Stieltjes series. Ukr Math J 45, 1636–1643 (1993). https://doi.org/10.1007/BF01571097

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  • DOI: https://doi.org/10.1007/BF01571097

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