Heisenberg Uncertainty Principle for the q-Bessel Fourier transform

2007/07/10 by Dhaouadi, Lazhar
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0707.1494

Abstract

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the q-Bessel Fourier transform: F_q,vf(x)=c_q,v∫₀^∞f(t)j_v(xt,q²)t^{2v +1}d_qt, where j_v(x,q) is the normalized Hahn-Exton q-Bessel function.

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