| 摘 要： | In approximation theory the theorem of Kolmogorov concerning the comparison of derivatives of differentiable functions defined on the real line is well-known. It plays an important r le in establishing sharp inequalities between the norms of derivatives of a function. In this note we establish a comparison theorem of Kolmogorov type on a class of functions which are defined on the real line and can be continuated analytically in a stripped region containing the real llne. As a consequence we have derived an inequality of Landau-Kolmogorov type on this function class, and moreover, we have applied it to get the exact estimation for the Kolmogorov's N-widths of the analytic function class.
|
