2017
Том 69
№ 6

# Order estimates for the approximative characteristics of functions from the classes $S_{p,θ}^{Ω} B(R^d)$ with a given majorant of generalized mixed modules of smoothness in the uniform metric

Yanchenko S. Ya.

Abstract

We establish the exact-order estimates of approximation for the classes $S_{p,θ}^{Ω} B$ of functions of several variables defined on $R^d$ in the norm of $L_{\infty} (R^d)$ by entire functions of exponential type with supports of their Fourier transforms in the sets generated by the level surfaces of a function $\Omega$.

Citation Example: Yanchenko S. Ya. Order estimates for the approximative characteristics of functions from the classes $S_{p,θ}^{Ω} B(R^d)$ with a given majorant of generalized mixed modules of smoothness in the uniform metric // Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1705-1714.