SHARP KOLMOGOROV-TYPE INEQUALITIES FOR MODULI OF CONTINUITY AND BEST APPROXIMATIONS BY TRIGONOMETRIC POLYNOMIALS AND SPLINES

摘要

In what follows, we use the following notation. We denote by R, Z, Z_+, and N the sets of real numbers, integers, nonriegative integers, and positive integers, respectively; unless otherwise implied by the context, all the functions considered can be either real-valued or complex-valued; C is the space of 2π-periodic continuous functions with the uniform norm; for r ∈ Z_+, C~((r)) denotes the subspace of C consisting of the functions that are r times continuously differentiable.