A noncommutative extension of Mahler’s interpolation theorem

Journal of noncommutative geometry

article

Jean-Éric Pin¹  Christophe Reutenauer² 

[1] Université de Paris et CNRS;Université du Québec à Montréal

关键词: Noncommutative algebra;    free group;    free monoid;    Magnustransformation;    subword functions;    sequential functions;    noncommutative polynomial functions;    p-groups;    noncommutative interpolation;    Mahler’s interpolation theorem;    p-adic;    difference operator;    forward difference formula;    combinatoricson words;   

DOI  :  10.4171/jncg/480

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

We prove a noncommutative generalization of Mahler’s theorem on interpolation series, a celebrated result of ppp-adic analysis. Mahler’s original result states that a function from N\mathbb{N}N to Z\mathbb{Z}Z is uniformly continuous for the ppp-adic metric dpd_pdp​ 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 F(B)F(B)F(B) where dpd_pdp​ is replaced by the pro-ppp metric.

【 授权许可】

CC BY