Multiparameter inverse problem of approximation by functions with given supports

  • A. N. Nesterenko
  • G. V. Radzievskii


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 $L_2$.
How to Cite
NesterenkoA. N., and RadzievskiiG. V. “Multiparameter Inverse Problem of Approximation by Functions With Given Supports”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 8, Aug. 2006, pp. 1116–1127,
Research articles