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

Amit Ophir; Ehud De Shalit

doi:https://doi.org/10.1093/qmath/haw035

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

Amit Ophir, Ehud De Shalit

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Q-Binomials and non-continuity of the p-adic fourier transform",

abstract = "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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AU - De Shalit, Ehud

PY - 2016/12/1

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N2 - 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.

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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U2 - https://doi.org/10.1093/qmath/haw035

DO - https://doi.org/10.1093/qmath/haw035

M3 - مقالة

SN - 0033-5606

VL - 67

SP - 653

EP - 668

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 4

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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