Let H1 be the 3-dimensional Heisenberg group. We prove that a modi-fied 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 jmj of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H1.
Astengo, F., Ricci, F., DI BLASIO, B. (2013). Fourier transform of Schwartz functions on the Heisenberg group. STUDIA MATHEMATICA, 214(3), 201-222 [10.4064/sm214-3-1].
Fourier transform of Schwartz functions on the Heisenberg group
DI BLASIO, BIANCA
2013
Abstract
Let H1 be the 3-dimensional Heisenberg group. We prove that a modi-fied 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 jmj of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H1.
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