Hyperdifferential Operators and Continuous Functions on Function Fields

Abstract We prove that a sequence of hyperdifferential operators is an orthonormal basis of the space of continuous F q-linear functions on F q[[T]]. By Conrad's 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 F q[[T]]. We then give the explicit derivation of the formula for digit derivative coefficients.

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