Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$

Authors

  • K.V. Pozharska Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine
  • 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
https://doi.org/10.15330/cmp.16.2.351-366

Keywords:

Sobolev class, Nikol'skii-Besov class, entropy number, width
Published online: 2024-07-08

Abstract

Exact-order estimates are obtained for the entropy numbers and several types of widths (Kolmogorov, linear, trigonometric and orthowidth) for the Sobolev and Nikol'skii-Besov classes of one and several variables in the space $B_{q,1}$, $1 <q< \infty$. It is shown, that in the multivariate case, in contrast to the univariate, the obtained estimates differ in order from the corresponding estimates in the space $L_q$.

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How to Cite
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Pozharska, K.; Romanyuk, A.; Romanyuk, V. Widths and Entropy Numbers of the Classes of Periodic Functions of One and Several Variables in the Space $B_{q,1}$. Carpathian Math. Publ. 2024, 16, 351-366.