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

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Trigonometric Sums and Their Applications

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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 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.

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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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Authors and Affiliations

  1. Institute of Analysis and Number Theory, Graz University of Technology, Graz, Austria

    Tetiana A. Stepanyuk

  2. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria

    Tetiana A. Stepanyuk

  3. Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine

    Tetiana A. Stepanyuk

Authors
  1. Tetiana A. Stepanyuk
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Correspondence to Tetiana A. Stepanyuk .

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Editors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Moscow state University, Moscow, Russia, Buryat State University, Ulan-Ude, Russia, Caucasus Mathematical Center, Adyghe State University, Maykop, Russia

    Andrei Raigorodskii

  2. Institute of Mathematics, University of Zurich, Zurich, Switzerland, Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Institute for Advanced Study Program in Interdisciplinary Studies, Princeton, NJ, USA

    Michael Th. Rassias

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Stepanyuk, T.A. (2020). Order Estimates of Best Orthogonal Trigonometric Approximations of Classes of Infinitely Differentiable Functions. In: Raigorodskii, A., Rassias, M. (eds) Trigonometric Sums and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-37904-9_13

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