The Heisenberg group and the group Fourier transform of regular homogeneous distributions
Studia Mathematica, Tome 143 (2000) no. 3, pp. 251-266
We calculate the group Fourier transform of regular homogeneous distributions defined on the Heisenberg group, $H^n$. All such distributions can be written as an infinite sum of terms of the form $f(θ)\overline{w}^{-k}P(z)$, where $(z,t) ∈ ℂ^{n} × ℝ$, $w = |z|^2 - it$, $θ = arg(\overline{w/w)$ and P(z) is an element of an orthonormal basis for the spherical harmonics. The formulas derived give the Fourier transform of the distribution in terms of a smooth kernel of the variable θ and the Weyl correspondent of P.
@article{10_4064_sm_143_3_251_266,
author = {Susan Slome},
title = {The {Heisenberg} group and the group {Fourier} transform of regular homogeneous distributions},
journal = {Studia Mathematica},
pages = {251--266},
year = {2000},
volume = {143},
number = {3},
doi = {10.4064/sm-143-3-251-266},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-143-3-251-266/}
}
TY - JOUR AU - Susan Slome TI - The Heisenberg group and the group Fourier transform of regular homogeneous distributions JO - Studia Mathematica PY - 2000 SP - 251 EP - 266 VL - 143 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-143-3-251-266/ DO - 10.4064/sm-143-3-251-266 LA - en ID - 10_4064_sm_143_3_251_266 ER -
%0 Journal Article %A Susan Slome %T The Heisenberg group and the group Fourier transform of regular homogeneous distributions %J Studia Mathematica %D 2000 %P 251-266 %V 143 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-143-3-251-266/ %R 10.4064/sm-143-3-251-266 %G en %F 10_4064_sm_143_3_251_266
Susan Slome. The Heisenberg group and the group Fourier transform of regular homogeneous distributions. Studia Mathematica, Tome 143 (2000) no. 3, pp. 251-266. doi: 10.4064/sm-143-3-251-266
Cité par Sources :