The Heisenberg group and the group Fourier transform of regular homogeneous distributions
Studia Mathematica, Tome 143 (2000) no. 3, pp. 251-266
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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},
publisher = {mathdoc},
volume = {143},
number = {3},
year = {2000},
doi = {10.4064/sm-143-3-251-266},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-143-3-251-266/}
}
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%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 %I mathdoc %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
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