Displaying similar documents to “On Heisenberg and local uncertainty principles for the q -Dunkl transform.”

Inequalities in q -Fourier analysis.

Dhaouadi, Lazhar, Fitouhi, Ahmed, El Kamel, J. (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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Fourier transform of Schwartz functions on the Heisenberg group

Francesca Astengo, Bianca Di Blasio, Fulvio Ricci (2013)

Studia Mathematica

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Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.