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Jean-Éric Pin, Pedro V. Silva

A noncommutative extension of Mahler’s theorem on interpolation series

European J. Combin., 36, 564-578 (2014)

http://dx.doi.org/10.1016/j.ejc.2013.09.009

Abstract

In this paper, we prove an extension of Mahler’s theorem on interpolation series, a celebrated result of p-adic analysis. Mahler’s original result states that a function from N to Z is uniformly continuous for the p-adic metric dp if and only if it can be uniformly approximated by polynomial functions. We prove the same result for functions from a free monoid A∗ to Z, where dp is replaced by the pro-p metric, the profinite metric on A∗ defined by p-groups.