Hyperdifferential Operators and Continuous Functions on Function Fields Original Research Article

We prove that a sequence of hyperdifferential operators is an orthonormal basis of the space of continuous imageq-linear functions on imageq[[T]]. By Conradʹs digit principle, the q-adic extensions of this sequence, called the digit derivatives, turn out to be an orthonormal basis of the whole space of continuous functions on imageq[[T]]. We then give the explicit derivation of the formula for digit derivative coefficients.