A noncommutative extension of Mahler’s interpolation theorem
Jean-Éric Pin
Université de Paris et CNRS, FranceChristophe Reutenauer
Université du Québec à Montréal, Canada
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