Geodesic
Fourier transform of Schwartz functions on the Heisenberg group
Francesca Astengo1 ; Bianca Di Blasio2 ; Fulvio Ricci3
1 Dipartimento di Matematica Università di Genova Via Dodecaneso 35 16146 Genova, Italy
2 Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca Via Cozzi 53 20125 Milano, Italy
3 Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italy
Studia Mathematica, Tome 214 (2013) no. 3, pp. 201-222 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\mathcal S_m(H_1)$ of Schwartz functions of type $m$ and the space $\mathcal S(\varSigma _m)$ consisting of restrictions of Schwartz functions on $\mathbb R^2$ to a subset $\varSigma _m$ 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 $H_1$.
DOI : 10.4064/sm214-3-1
Keywords: dimensional heisenberg group prove modified version spherical transform isomorphism between space mathcal schwartz functions type space mathcal varsigma consisting restrictions schwartz functions mathbb subset varsigma heisenberg fan half lines removed result applied study general schwartz functions nbsp

Francesca Astengo 1 ; Bianca Di Blasio 2 ; Fulvio Ricci 3

1 Dipartimento di Matematica Università di Genova Via Dodecaneso 35 16146 Genova, Italy
2 Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca Via Cozzi 53 20125 Milano, Italy
3 Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italy 
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     title = {Fourier transform of {Schwartz} functions
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Francesca Astengo; Bianca Di Blasio; Fulvio Ricci. Fourier transform of Schwartz functions
 on the Heisenberg group. Studia Mathematica, Tome 214 (2013) no. 3, pp. 201-222. doi: 10.4064/sm214-3-1

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