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

T. Godoy; L. Saal

Colloquium Mathematicae (2006)

  • Volume: 106, Issue: 2, page 231-255
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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T. Godoy, and L. Saal. "A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)." Colloquium Mathematicae 106.2 (2006): 231-255. <http://eudml.org/doc/284345>.

@article{T2006,
abstract = {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.},
author = {T. Godoy, L. Saal},
journal = {Colloquium Mathematicae},
keywords = {Heisenberg group; spherical transform; Schwartz space},
language = {eng},
number = {2},
pages = {231-255},
title = {A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)},
url = {http://eudml.org/doc/284345},
volume = {106},
year = {2006},
}

TY - JOUR
AU - T. Godoy
AU - L. Saal
TI - A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 2
SP - 231
EP - 255
AB - 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.
LA - eng
KW - Heisenberg group; spherical transform; Schwartz space
UR - http://eudml.org/doc/284345
ER -

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