ON -WIDTHS, OPTIMAL QUADRATURE FORMULAS, AND OPTIMAL RECOVERY OF FUNCTIONS ANALYTIC IN A STRIP

Abstract

Let be the space of bounded analytic functions in the strip . We denote by the set of -periodic functions in , and by the set of functions in that are real on the real axis. For a normed linear space we set . In this paper the exact values of the Kolmogorov -widths , are found for all , an optimal quadrature formula is constructed for the class by using the values of functions defined with an error and it is proved that the unique (to within a shift) optimal system of nodes is given by a uniform net. In addition to this, a number of problems are solved for the optimal recovery of functions and their derivatives in the class .