A noncommutative extension of Mahler’s interpolation theorem

  • Jean-Éric Pin

    Université de Paris et CNRS, France
  • Christophe Reutenauer

    Université du Québec à Montréal, Canada
A noncommutative extension of Mahler’s interpolation theorem cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

We prove a noncommutative generalization of Mahler’s theorem on interpolation series, a celebrated result of -adic analysis. Mahler’s original result states that a function from to is uniformly continuous for the -adic metric if and only if it can be uniformly approximated by polynomial functions. We prove an analogous result for functions from a free monoid A to a free group where is replaced by the pro- metric.

Cite this article

Jean-Éric Pin, Christophe Reutenauer, A noncommutative extension of Mahler’s interpolation theorem. J. Noncommut. Geom. 16 (2022), no. 3, pp. 1055–1101

DOI 10.4171/JNCG/480