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Order Estimates of Best Orthogonal Trigonometric Approximations of Classes of Infinitely Differentiable Functions

  • Tetiana A. StepanyukEmail author
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Abstract

In this paper we establish exact order estimates for the best uniform orthogonal trigonometric approximations of the classes of 2π-periodic functions, whose (ψ, β)–derivatives belong to unit balls of spaces Lp, 1 ≤ p < , in the case, when the sequence ψ(k) tends to zero faster, than any power function, but slower than geometric progression. Similar estimates are also established in the Ls-metric, 1 < s ≤, for the classes of differentiable functions, which (ψ, β)–derivatives belong to unit ball of space L1.

Keywords

Fourier series Best orthogonal trigonometric approximation Classes of infinitely differentiable functions (ψ, β)-derivative 

Notes

Acknowledgements

The author is supported by the Austrian Science Fund FWF projects F5503 and F5506-N26 (part of the Special Research Program (SFB) “Quasi-Monte Carlo Methods: Theory and Applications”) and partially is supported by grant of NAS of Ukraine for groups of young scientists (project No16-10/2018).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Analysis and Number TheoryGraz University of TechnologyGrazAustria
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  3. 3.Institute of Mathematics of NAS of UkraineKyivUkraine

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