Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form


  • S.Ya. Yanchenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, Ukraine


Nikol'skii-Besov classes, entire functions of exponential type, Fourier transform
Published online: 2020-06-12


We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta}B(\mathbb{R}^d)$, $d\geq 1$, by entire functions of exponential type with some restrictions for their spectrum. The error of the approximation is estimated in the metric of the Lebesgue space $L_{\infty}(\mathbb{R}^d)$.

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How to Cite
Yanchenko, S. Approximation of the Nikol’skii-Besov Functional Classes by Entire Functions of a Special Form. Carpathian Math. Publ. 2020, 12, 148-156.