Konareva S. Inequalities of Jackson type in Hilbert spaces

The dissertation is devoted to the questions about exact constants in Jackson - Stechkin type inequalities, which estimate the approximation of functions with values in Hilbert space and Hilbert space elements through their continuity modules, modules of smoothness, and generalized continuity modules. New exact Jackson-Stechkin type inequalities of the best approximation derivative of a function f with values in a separable Hilbert space by generalized trigonometric polynomials in terms of the modulus of continuity, the modulus of smoothness and generalized the modulus of continuity of the function itself were obtained. New exact Jackson type inequalities were obtained for functions with values in Hilbert space that are analytic in a single circle. Exact values of weak widths Kolmogorov of some classes of functions with values in separable Hilbert space were obtained. Exact Jackson-Stechkin type inequalities were obtained of the best approximation of almost periodic functions with values in Hilbert space. New exact estimates are obtained for the best approximation of elements of a separable Hilbert space H by subspaces generated by a given decomposition of unity through generalized the modulus of continuity of elements of this space. The accuracy conditions for these inequalities are indicated.