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On Best Harmonic Synthesis of Periodic Functions

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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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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Keywords

  • Lagrange Function
  • Recovery Method
  • Optimal Recovery
  • Admissible Sequence
  • Recovery Problem