Best approximation by ridge functions in $L_p$-spaces

• Дата: 2010
• Автори: Maiorov, V. E., Майоров, В. Є.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2010
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/2875
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We study the approximation of the classes of functions by the manifold $R_n$ formed by all possible linear combinations of $n$ ridge functions of the form $r(a · x))$. It is proved that, for any $1 ≤ q ≤ p ≤ ∞$, the deviation of the Sobolev class $W^r_p$ from the set $R_n$ of ridge functions in the...