q-BINOMIALS AND NON-CONTINUITY OF THE p-ADIC FOURIER TRANSFORM.

Let F be a finite extension of ℚp. We show that every Schwartz function on F, with values in ℚp, is the p-adic uniform limit of a sequence of Schwartz functions, whose Fourier transforms tend uniformly to 0. The proof uses the notion of q-binomial coefficients and some classical identities between these polynomials. [ABSTRACT FROM AUTHOR]