Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators

• Date: 1995
• Main Authors: Shabozov, M. Sh., Шабозов, М. Ш.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5546
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the classB p ρ , 0 ≤ ρ < 1, 1≤p ≤ ∞, of 2π-periodic functions of the form f(t)=u(ρ,t), whereu (ρ,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel Kρ(t) of the convolution f= Kρ *g, ∥g∥ρ≤l,...