A remark on Kolmogorov's comparison theorem (Q1093114)

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 rôle in establishing sharp inequalities between the norms of derivatives of a function. We establish a comparison theorem of Kolmogorov type on a class of functions which are defined on the real line and can be continued analytically in a stripped region containing the real line. As a consequence we derive an inequality of Landau-Kolmogorov type on this function class, and moreover, we apply it to get the exact estimation for Kolmogorov's N-widths of the analytic function class.