Kolmogorov problem on classes of absolute monotone and multiple monotone functions and its connection with Markov moment problem

TL;DR

This paper addresses the Kolmogorov problem for classes of absolute and multiple monotone functions, establishing existence conditions for functions with specified derivative norms and linking it to the Markov moment problem.

Contribution

It provides a solution to the Kolmogorov problem for multiple monotone and absolute monotone functions with arbitrary derivative norms, and connects it to the Markov moment problem.

Findings

Solved the Kolmogorov problem for multiple monotone functions.

Established the connection between Kolmogorov and Markov moment problems.

Extended results to arbitrary numbers of derivative norms.

Abstract

In this paper we solve Kolmogorov problem about existence of a function with given norms of derivatives for classes of multiple monotone functions and absolute monotone functions in the case of arbitrary number of norms. We also show the connection of Kolmogorov problem with Markov moment problem.