Geodesic
A spherical transform on Schwartz functions on the Heisenberg group associated to the action of $U(p,q)$
T. Godoy 1   ; L. Saal 2
1 FaMAF (Universidad Nacional de Córdoba) and CIEM-CONICET Ciudad Universitaria 5000 Córdoba, Argentina
2 FaMAF (Universidad Nacional de Córdoba) and CIEM-CONICET, Ciudad Universitaria 5000 Córdoba, Argentina
Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 231-255 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/cm106-2-5
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

T. Godoy  1   ; L. Saal  2

1 FaMAF (Universidad Nacional de Córdoba) and CIEM-CONICET Ciudad Universitaria 5000 Córdoba, Argentina
2 FaMAF (Universidad Nacional de Córdoba) and CIEM-CONICET, Ciudad Universitaria 5000 Córdoba, Argentina 
@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},
     year = {2006},
     volume = {106},
     number = {2},
     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
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
%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 :