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On Best Harmonic Synthesis of Periodic Functions

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Abstract

In this paper, we construct optimal methods of recovery of periodic functions from a known (exact or inexact) finite family of their Fourier coefficients. The proposed approach to constructing recovery methods is compared with the approach based on the Tikhonov regularization method.

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References

  1. V. A. Il’in and E. G. Poznyak, Foundations of Mathematical Analysis, Part II (in Russian), Nauka, Moscow (1973).

    Google Scholar 

  2. G. G. Magaril-Il’yaev and K. Yu. Osipenko, “Optimal recovery of functions and their derivatives from Fourier coefficients prescribed with an error,” Sb. Math., 193, No. 3, 387–407 (2002).

    Article  MathSciNet  Google Scholar 

  3. G. G. Magaril-Il’yaev and K. Yu. Osipenko, “Optimal recovery of functions and their derivatives from inaccurate information about the spectrum and inequalities for derivatives,” Funct. Anal. Appl., 37, No. 3, 203–214 (2003).

    Article  MathSciNet  Google Scholar 

  4. G. G. Magaril-Il’yaev and K. Yu. Osipenko, “Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform,” Sb. Math., 195, No. 10, 1461–1476 (2004).

    Article  MathSciNet  Google Scholar 

  5. G. G. Magaril-Il’yaev and K. Yu. Osipenko, “On optimal harmonic synthesis from inaccurate spectral data,” Funct. Anal. Appl., 44, No. 3, 223–225 (2010).

    Article  MathSciNet  Google Scholar 

  6. G. G. Magaril-Il’yaev and K. Yu. Osipenko, “How best to recover a function from its inaccurately given spectrum?” Math. Notes, 92, No. 1, 51–58 (2012).

    Article  MathSciNet  Google Scholar 

  7. G. G. Magaril-Il’yaev and E. O. Sivkova, “Best recovery of the Laplace operator of a function from incomplete spectral data,” Sb. Math., 203, No. 4, 569–580 (2012).

    Article  MathSciNet  Google Scholar 

  8. E. O. Sivkova, “On optimal recovery of the Laplacian of a function from its inaccurately given Fourier transform,” Vladikavkaz. Mat. Zh., 14, No. 4, 63–72 (2012).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    G. G. Magaril-Il’yaev

  2. A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    G. G. Magaril-Il’yaev

  3. Moscow State Aviation Technological University, Moscow, Russia

    K. Yu. Osipenko

  4. South Mathematical Institute of Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, Russia

    K. Yu. Osipenko

Authors
  1. G. G. Magaril-Il’yaev
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  2. K. Yu. Osipenko
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Corresponding author

Correspondence to G. G. Magaril-Il’yaev.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 155–174, 2013.

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Magaril-Il’yaev, G.G., Osipenko, K.Y. On Best Harmonic Synthesis of Periodic Functions. J Math Sci 209, 115–129 (2015). https://doi.org/10.1007/s10958-015-2489-z

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  • DOI: https://doi.org/10.1007/s10958-015-2489-z

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