Fermat quotient operators and locally analytic functions

초록

Buium et al. characterized locally analytic functions on ${\mathbb{Z}}_p$ in terms of a restricted power series over ${\mathbb{Z}}_p$ with finitely many iterates of the Fermat quotient operator. In this paper we establish the function field analogue of their result. In addition, we deduce Wagner's result for continuous functions on completions of ${\text{F}}_r[T].$