Optimal Recovery of Analytic Functions

Contents: Preface; Optimal Recovery Settings and General Results -- A General Setting; Optimal Recovery of Multi-Valued Mappings; Optimal Recovery of Linear Functionals; Optimal Algorithms Using Fourier Coefficients. Optimal Recovery in Hp -- Optimal Recovery at a Fixed Point; The Periodic Case; Countable Sets of Nodes; Optimal Nodes; Functions of Several Variables. Optimal Recovery of Derivatives -- Optimal Recovery of the First Derivative; A General Case; The Periodic Case for the First Derivative; Noisy Information; Kolmogorov Inequalities. Exact n-Widths of Analytic Functions -- Exact n-Widths in Hp; Estimates of n-Widths for Hp in Lq(-1,1); Exact n-Widths of Periodic Functions; Estimations of n-Widths in Hilbert Spaces; Diagonal Operators; Hardy-Sobolev and Bergman-Sobolev Classes. Quadrature Formulas -- Best quadrature formulas in Hp; Optimal Quadrature Formulas; Estimates of Optimal Quadratures.