Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653630 | European Journal of Combinatorics | 2014 | 15 Pages |
Abstract
In this paper, we prove an extension of Mahler’s theorem on interpolation series, a celebrated result of pp-adic analysis. Mahler’s original result states that a function from NN to ZZ is uniformly continuous for the pp-adic metric dpdp if and only if it can be uniformly approximated by polynomial functions. We prove the same result for functions from a free monoid A∗A∗ to ZZ, where dpdp is replaced by the pro-pp metric, the profinite metric on A∗A∗ defined by pp-groups.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jean-Éric Pin, Pedro V. Silva,