Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville operator.
Omri, S., Rachdi, L.T. (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville operator.
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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.
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