## International Conference on $p$-ADIC MATHEMATICAL PHYSICS AND ITS APPLICATIONS $p$-ADICS.2015, 07-12.09.2015, Belgrade, Serbia

﻿ Enno Nagel

### The Fourier Basis of p-adic Differentiable Functions

Abstract

Having emerged from the $p$-adic Langlands program, $C^r$-functions over a $p$-adic number field for a real number $r \geq 0$ are introduced. Their dual, integrals on $C^r$-functions, identifies by evaluation on "Fourier polynomials" (brought about by Lubin-Tate theory) with power series convergent on the open unit disc.