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Growth of Norms in L 2 of Derivatives of the Steklov Functions and Properties Defined by the Best Approximations and Fourier Coefficients

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In the paper, for periodic functions, a connection between integrals of norms in L2 of derivatives of the Steklov functions and series constructed from Fourier coefficients and the best approximations in L2 is established, and the question on their simultaneous convergence or divergence is examined. Similar investigations are carried out for even and odd periodic functions. Bibliography: 13 titles.

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References

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Authors and Affiliations

  1. St.Petersburg State University, St.-Petersburg, Russia

    M. V. Babushkin & V. V. Zhuk

Authors
  1. M. V. Babushkin
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  2. V. V. Zhuk
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Correspondence to M. V. Babushkin or V. V. Zhuk.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 445, 2016, pp. 5–32.

Translated by L. Yu. Kolotilina.

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Babushkin, M.V., Zhuk, V.V. Growth of Norms in L 2 of Derivatives of the Steklov Functions and Properties Defined by the Best Approximations and Fourier Coefficients. J Math Sci 222, 525–543 (2017). https://doi.org/10.1007/s10958-017-3320-9

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  • DOI: https://doi.org/10.1007/s10958-017-3320-9

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