Multiparameter inverse problem of approximation by functions with given supports

• Date: 2006
• Main Authors: Nesterenko, A. N., Radzievskii, G. V., Нестеренко, А. Н., Радзиевский, Г. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3517
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $L_p(S),\;0 < p < +∞$, be a Lebesgue space of measurable functions on $S$ with ordinary quasinorm $∥·∥_p$. For a system of sets $\{B t |t ∈ [0, +∞)^n \}$ and a given function $ψ: [0, +∞) n ↦ [ 0, +∞)$, we establish necessary and sufficient conditions for the existence of a function...