Best mean-square approximation of functions defined on the real axis by entire functions of exponential type

  • S. B. Vakarchuk Днепропетр. ун-т им. А. Нобеля

Abstract

Exact constants in Jackson-type inequalities are calculated in the space $L_2 (\mathbb{R})$ in the case where the quantity of the best approximation $\mathcal{A}_{\sigma}(f)$ is estimated from above by the averaged smoothness characteristic $\Phi_2(f, t) = \cfrac 1t \int^t_0||\Delta^2_h(f)||dh$. We also calculate the exact values of the average $\nu$-widths of classes of functions defined by $\Phi_2$.
Published
25.05.2012
How to Cite
VakarchukS. B. “Best Mean-Square Approximation of Functions Defined on the Real Axis by Entire Functions of Exponential Type”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 5, May 2012, pp. 604-15, http://umj.imath.kiev.ua/index.php/umj/article/view/2601.
Section
Research articles