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Let F be a finite extension of Q_p. We show that every Schwartz function onF, with values in an algebraic closure of Q_p, is the uniform limit of asequence of Schwartz functions, whose Fourier transforms tend uniformly to 0.The proof uses the notion of q-binomial coefficients and some classicalidentities between them.

Q-binomials and non-continuity of the p-adic Fourier transform