Kolmogorov problem on the class of multiply monotone functions

Oleg Kovalenko

paper

Kolmogorov problem on the class of multiply monotone functions

arXiv:1401.2923

Abstract

Necessary and sufficient conditions for positive numbers $M_{k_{1}}, M_{k_{2}}, M_{k_{3}}, M_{k_{4}}$ , $0 = k_{1} < k_{2} < k_{2} \leq r - 2$ , $k_{4} = r$ , to guarantee the existence of an $r - 1$ -monotone function defined on the negative half-line and such that $∥ x^{(k_{i})} ∥ = M_{k_{i}}$ , $i = 1, 2, 3, 4$ were found.

5 pages in English and 6 pages in Russian