Heisenberg Uncertainty Principle for the q-Bessel Fourier transform

Details Heisenberg Uncertainty Principle for the q-Bessel Fourier transform Heisenberg Uncertainty Principle for the q-Bessel Fourier transform

2007-07-10

arxiv.org/abs/0707.1494v2

Mathematics

Classical Analysis and ODEs

Scientific paper

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give
an uncertainty inequality for the $q$-Bessel Fourier transform: $$
\mathcal{F}_{q,v}f(x)=c_{q,v}\int_{0}^{\infty}f(t)j_{v}(xt,q^{2})t^{2v
+1}d_{q}t, $$ where $j_v(x,q)$ is the normalized Hahn-Exton $q$-Bessel
function.

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