TY - JOUR
AU - S. B. Vakarchuk
PY - 2012/05/25
Y2 - 2024/06/23
TI - Best mean-square approximation of functions defined on the real axis by entire functions of exponential type
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 64
IS - 5
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2601
AB - Exact constants in Jackson-type inequalities are calculated in the space $L_2 (\mathbb{R})$ in the case where the quantity of the bestapproximation $\mathcal{A}_{\sigma}(f)$ 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 $
u$-widths of classes of functions defined by $\Phi_2$.
ER -