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Addendum to “Trigonometric series of Nikol’skii classes”

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Abstract

We describe the functions from Nikol’skii class in terms of behavior of their Fourier coefficients. Results for series with general monotone coefficients are presented. The problem of strong approximation of Fourier series is also studied.

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References

  1. P. L. Butzer, H. Dyckhoff, E. Göerlich and R. L. Stens, Best trigonometric approximation, fractional order derivatives and Lipschitz classes, Can. J. Math., 29 (1977), 781–793.

    MATH  Google Scholar 

  2. M. Dyachenko and S. Tikhonov, Convergence of trigonometric series with general monotone coefficients, C.R. Acad. Sci. Paris, Ser. I, 345 (2007), 123–126.

    MATH  MathSciNet  Google Scholar 

  3. R. J. Le and S. P. Zhou, A new condition for the uniform convergence of certain trigonometric series, Acta Math. Hungar., 108 (2005), 161–169.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Leindler, Strong Approximation by Fourier Series (Budapest, 1985).

  5. L. Leindler, Embedding results regarding strong approximation of sine series, Acta Sci. Math. (Szeged), 71 (2005), 91–103.

    MATH  MathSciNet  Google Scholar 

  6. S. Tikhonov, Trigonometric series of Nikol’skii classes, Acta Math. Hungar., 114 (2007), 61–78.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Tikhonov, Trigonometric series with general monotone coefficients, J. Math. Anal. Appl., 326 (2007), 721–735.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Tikhonov, Embedding results in questions of strong approximation by Fourier series, Acta Sci. Math. (Szeged), 72 (2006), 117–128.

    MATH  MathSciNet  Google Scholar 

  9. S. Tikhonov, Best approximation and moduli of smoothness: computation and equivalence theorems, to appear in J. Approx. Theory.

  10. D. S. Yu and S. P. Zhou, A generalization of monotonicity condition and applications, Acta Math. Hungar., 115 (2007), 247–267.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. P. Zhou, P. Zhou and D. S. Yu, Ultimate generalization to monotonicity for uniform convergence of trigonometric series, arXiv:math.CA/0611805 v1 27 Nov 2006.

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Authors and Affiliations

  1. Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, 56126, Italy

    S. Tikhonov

  2. ICREA and Centre de Recerca Matemàtica, Apartat 50, E-08193, Barcelona, Spain

    S. Tikhonov

Authors
  1. S. Tikhonov
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Correspondence to S. Tikhonov.

Additional information

This work was partially supported by the Russian Foundation for Fundamental Research (grant no. 06-01-00268) and the Leading Scientific Schools (grant NSH-2787.200 1). The paper was written while the author was staying at the Scuola Normale Superiore.

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Tikhonov, S. Addendum to “Trigonometric series of Nikol’skii classes”. Acta Math Hung 120, 9–20 (2008). https://doi.org/10.1007/s10474-008-7074-1

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  • DOI: https://doi.org/10.1007/s10474-008-7074-1

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