Let H_1 be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space S_m(H_1) of Schwartz functions of type m and the space S(\Sigma_m) consisting of restrictions of Schwartz functions on R^2 to a subset \Sigma_m 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 H_1.

Fourier transform of Schwartz functions on the Heisenberg group

ASTENGO, FRANCESCA;
2013

Abstract

Let H_1 be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space S_m(H_1) of Schwartz functions of type m and the space S(\Sigma_m) consisting of restrictions of Schwartz functions on R^2 to a subset \Sigma_m 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 H_1.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/578143
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