A spherical transform on Schwartz functions
on the Heisenberg group associated to the action of $U(p,q)$
Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 231-255
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
mathcal space schwartz functions heisenberg group define spherical transform mathcal associated action automorphisms determine its kernel image obtain inversion formula analogous godement plancherel formula
Affiliations des auteurs :
T. Godoy 1 ; L. Saal 2
@article{10_4064_cm106_2_5,
author = {T. Godoy and L. Saal},
title = {A spherical transform on {Schwartz} functions
on the {Heisenberg} group associated to the action of $U(p,q)$},
journal = {Colloquium Mathematicum},
pages = {231--255},
publisher = {mathdoc},
volume = {106},
number = {2},
year = {2006},
doi = {10.4064/cm106-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-5/}
}
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 Mathematicum PY - 2006 SP - 231 EP - 255 VL - 106 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-5/ DO - 10.4064/cm106-2-5 LA - en ID - 10_4064_cm106_2_5 ER -
%0 Journal Article %A T. Godoy %A L. Saal %T A spherical transform on Schwartz functions on the Heisenberg group associated to the action of $U(p,q)$ %J Colloquium Mathematicum %D 2006 %P 231-255 %V 106 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-5/ %R 10.4064/cm106-2-5 %G en %F 10_4064_cm106_2_5
T. Godoy; L. Saal. A spherical transform on Schwartz functions on the Heisenberg group associated to the action of $U(p,q)$. Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 231-255. doi: 10.4064/cm106-2-5
Cité par Sources :