Abstract
We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{\beta,p}, 1\le p\le\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\rightarrow\infty)$ in the uniform metric. We obtain similar estimates for approximations of the classes $W^r_{\beta,1}$ in metrics of the spaces $L_p, 1\le p\le\infty$.
Key words: Fourier sum, Weyl-Nagy class, asymptotic equality.
Full Text
Article Information
| Title | Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness |
| Source | Methods Funct. Anal. Topology, Vol. 25 (2019), no. 4, 381-387 |
| MathSciNet |
MR4049692 |
| Milestones | Received 21/05/2019 |
| Copyright | The Author(s) 2019 (CC BY-SA) |
Authors Information
A. S. Serdyuk
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine
I. V. Sokolenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine
Citation Example
A. S. Serdyuk and I. V. Sokolenko, Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness, Methods Funct. Anal. Topology 25
(2019), no. 4, 381-387.
BibTex
@article {MFAT1245,
AUTHOR = {A. S. Serdyuk and I. V. Sokolenko},
TITLE = {Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {4},
PAGES = {381-387},
ISSN = {1029-3531},
MRNUMBER = {MR4049692},
URL = {http://mfat.imath.kiev.ua/article/?id=1245},
}
