Heisenberg Uncertainty Principle for the q-Bessel Fourier transform

Lazhar Dhaouadi (1)

1 Analyse harmonique et fonctions spéciales

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.

Mots clés: Heisenberg Uncertainty Principle; q-Bessel Fourier transform

Domaines: Analyse classique [math.CA]; Mathématiques générales [math.GM]

Lazhar Dhaouadi. Heisenberg Uncertainty Principle for the q-Bessel Fourier transform. 2007. ⟨hal-00161302v2⟩