On an Example of the Nikishin System

S. P. Suetin

Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 918-929.

Résumé

An example of a Markov function $f=\mathrm{const}+\widehat{\sigma}$ such that the three functions $f$, $f^2$, and $f^3$ constitute a Nikishin system is given. It is conjectured that there exists a Markov function $f$ such that, for each $n\in\mathbb N$, the system of $f,f^2,\dots,f^n$ is a Nikishin system.

Détail

Keywords: Hermite–Padé polynomials, Angelesco system, Nikishin system.

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