Q-Binomials and non-continuity of the p-adic fourier transform

Amit Ophir; Ehud De Shalit

doi:10.1093/qmath/haw035

Q-Binomials and non-continuity of the p-adic fourier transform

Amit Ophir, Ehud De Shalit^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let F be a finite extension of Q_p. We show that every Schwartz function on F, with values in Q_p, 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.

Original language	English
Pages (from-to)	653-668
Number of pages	16
Journal	Quarterly Journal of Mathematics
Volume	67
Issue number	4
DOIs	https://doi.org/10.1093/qmath/haw035
State	Published - 1 Dec 2016

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© 2016. Published by Oxford University Press. All rights reserved.

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AB - 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.

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Q-Binomials and non-continuity of the p-adic fourier transform

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