Trigonometric Sums and Their Applications pp 273-287 | Cite as

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

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## Abstract

In this paper we establish exact order estimates for the best uniform orthogonal trigonometric approximations of the classes of 2*π*-periodic functions, whose (*ψ*, *β*)–derivatives belong to unit balls of spaces *L*_{p}, 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 *L*_{s}-metric, 1 < *s* ≤*∞*, for the classes of differentiable functions, which (*ψ*, *β*)–derivatives belong to unit ball of space *L*_{1}.

## 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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