A noncommutative extension of Mahler's theorem on interpolation series - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2011

A noncommutative extension of Mahler's theorem on interpolation series

Résumé

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 d_p 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 d_p is replaced by the pro-p metric, the profinite metric on A* defined by p-groups.
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Dates et versions

hal-00654030 , version 1 (20-12-2011)

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  • HAL Id : hal-00654030 , version 1

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Jean-Eric Pin, Pedro Silva. A noncommutative extension of Mahler's theorem on interpolation series. 2011. ⟨hal-00654030⟩
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