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arXiv · 1607.03670

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

Amit Ophir·Ehud de Shalit
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Abstract

Let F be a finite extension of Q_p. We show that every Schwartz function on F, with values in an algebraic closure of Q_p, is the 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 them.

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Amit Ophir, Ehud de Shalit. 2016-07-13. Q-binomials and non-continuity of the p-adic Fourier transform. https://arxiv.org/abs/1607.03670

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