A spherical transform on Schwartz functions
 on the Heisenberg  group associated to the action of $U(p,q)$

T. Godoy; L. Saal

doi:10.4064/cm106-2-5

Geodesic

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A spherical transform on Schwartz functions on the Heisenberg group associated to the action of $U(p,q)$

T. Godoy ¹ ; L. Saal ²

¹ FaMAF (Universidad Nacional de Córdoba) and CIEM-CONICET Ciudad Universitaria 5000 Córdoba, Argentina
² FaMAF (Universidad Nacional de Córdoba) and CIEM-CONICET, Ciudad Universitaria 5000 Córdoba, Argentina

Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 231-255.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

Let $\mathcal{S}(H_{n})$ be the space of Schwartz functions on the Heisenberg group $H_{n}$. We define a spherical transform on $\mathcal{S}(H_{n})$ associated to the action (by automorphisms) of $U(p,q)$ on $H_{n}$, $p + q = n$. We determine its kernel and image and obtain an inversion formula analogous to the Godement–Plancherel formula.

DOI : 10.4064/cm106-2-5

Keywords: mathcal space schwartz functions heisenberg group define spherical transform mathcal associated action automorphisms determine its kernel image obtain inversion formula analogous godement plancherel formula

Affiliations des auteurs :

T. Godoy ¹ ; L. Saal ²

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T. Godoy; L. Saal. A spherical transform on Schwartz functions
 on the Heisenberg  group associated to the action of $U(p,q)$. Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 231-255. doi : 10.4064/cm106-2-5. http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-5/

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