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

Volume 106 / 2006

T. Godoy, L. Saal Colloquium Mathematicum 106 (2006), 231-255 MSC: Primary 43A80; Secondary 22E25. DOI: 10.4064/cm106-2-5

Abstract

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.

Authors

  • T. GodoyFaMAF (Universidad Nacional de Córdoba) and
    CIEM-CONICET
    Ciudad Universitaria
    5000 Córdoba, Argentina
    e-mail
  • L. SaalFaMAF (Universidad Nacional de Córdoba) and
    CIEM-CONICET,
    Ciudad Universitaria
    5000 Córdoba, Argentina
    e-mail

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