TY - JOUR
AU - A. N. Nesterenko
AU - G. V. Radzievskii
PY - 2006/08/25
Y2 - 2024/08/06
TI - Multiparameter inverse problem of approximation by functions with given supports
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 58
IS - 8
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3517
AB - 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 $f ∈ L_p(S)$ such that $\inf \{∥f − g∥^p_p| g ∈ L_p(S),\;g = 0$ almost everywhere on $S\B t } = ψ (t), t ∈ [0, +∞)^n$. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation by functions of the exponential type in $L_2$.
ER -