Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

Authors

  • A.S. Romanyuk Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine https://orcid.org/0000-0002-6268-0799
  • V.S. Romanyuk Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine
  • K.V. Pozharska Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine https://orcid.org/0000-0001-7599-8117
  • S.B. Hembars'ka Lesya Ukrainka Volyn National University, 13 Voli ave., 43025, Lutsk, Ukraine
https://doi.org/10.15330/cmp.15.1.78-94

Keywords:

Nikol'skii-Besov class, best orthogonal trigonometric approximation, best approximation, width
Published online: 2023-06-14

Abstract

Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $\mathbf{B}^r_{p,\theta}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1\leq q \leq \infty$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths.

For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1<p<2\leq q < \frac{p}{p-1}$) are realized by the approximation of functions from the classes ${\mathbf{B}}^r_{p,\theta}$ by trigonometric polynomials with the spectrum in cubic regions. In any case, they do not depend on the smoothness parameter $\theta$.

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How to Cite
(1)
Romanyuk, A.; Romanyuk, V.; Pozharska, K.; Hembars'ka, S. Characteristics of Linear and Nonlinear Approximation of Isotropic Classes of Periodic Multivariate Functions. Carpathian Math. Publ. 2023, 15, 78-94.

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