Kolmogorov's Problem on the Class of Multiply Monotone Functions

Vladyslav Babenko; Yuliya Babenko; Oleg Kovalenko

paper

Kolmogorov's Problem on the Class of Multiply Monotone Functions

arXiv:1308.5268

Abstract

In this paper we give necessary and sufficient conditions for the system of positive numbers $M_{k_{1}}, M_{k_{2}}, ..., M_{k_{d}},$ $0 \leq k_{1} < ... < k_{d} \leq r$ , to guarantee the existence of an $r$ -monotone function defined on the negative half-line $\RR_-$ and such that $∥ x^{(k_{i})} ∥_{\infty} = M_{k_{i}}, i = 1, 2, ..., d$ .

24 pages