On one example of a Nikishin system

Abstract

The paper puts forward an example of a~Markov function $f=\operatorname{const}+\widehat{\sigma}$ such that the three functions $f,f^2$ and $f^3$ form a Nikishin system. A conjecture is proposed that there exists a~Markov function $f$ such that, for each $n\in\mathbb N$, the system $f,f^2,\dots,f^n$ constitutes a~Nikishin system. Bibliography:~20~titles.