A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)
T. Godoy ; L. Saal
Colloquium Mathematicae, Tome 106 (2006), p. 231-255 / Harvested from The Polish Digital Mathematics Library
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Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:284345 
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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 Mathematicae, Tome 106 (2006) pp. 231-255. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-5/