Kolmogorov's problem for completely and multiply monotone functions and the Markov moment problem

TL;DR

This paper solves Kolmogorov's problem for multiply and completely monotone functions, linking it to the Markov moment problem and other extremal problems, advancing understanding in function approximation and extremal analysis.

Contribution

It provides the first comprehensive solution to Kolmogorov's problem for these classes of functions and explores their connections to classical extremal problems.

Findings

Solution to Kolmogorov's problem for multiply and completely monotone functions

Connections established with the Markov moment problem and Hermite-Birkhoff interpolation

Enhanced understanding of extremal properties of monotone functions

Abstract

In this paper, we present the solution to Kolmogorov's problem for the classes of multiply monotone and completely monotone functions together with its connections to the Markov moment problem, Hermite-Birkhoff interpolation problem, and other extremal problems.