Fourier transform of Schwartz functions on the Heisenberg group

Francesca Astengo, Bianca Di Blasio, and Fulvio Ricci. "Fourier transform of Schwartz functions on the Heisenberg group." Studia Mathematica 214.3 (2013): 201-222. <http://eudml.org/doc/286265>.

@article{FrancescaAstengo2013,
abstract = {Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ 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 H₁.},
author = {Francesca Astengo, Bianca Di Blasio, Fulvio Ricci},
journal = {Studia Mathematica},
keywords = {Fourier transform; Schwartz space; Heisenberg group},
language = {eng},
number = {3},
pages = {201-222},
title = {Fourier transform of Schwartz functions on the Heisenberg group},
url = {http://eudml.org/doc/286265},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Francesca Astengo
AU - Bianca Di Blasio
AU - Fulvio Ricci
TI - Fourier transform of Schwartz functions on the Heisenberg group
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 3
SP - 201
EP - 222
AB - Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ 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 H₁.
LA - eng
KW - Fourier transform; Schwartz space; Heisenberg group
UR - http://eudml.org/doc/286265
ER -