We formulate and prove a version of Paley-Wiener theorem for the inverse Fourier transforms on noncompact Riemannian symmetric spaces and Heisenberg groups. The main ingredient in the proof is the Gutzmer’s formula.
@article{1187916316,
author = {Thangavelu, S.},
title = {A Paley-Wiener theorem for the inverse Fourier transform on some homogeneous spaces},
journal = {Hiroshima Math. J.},
volume = {37},
number = {1},
year = {2007},
pages = { 145-159},
language = {en},
url = {http://dml.mathdoc.fr/item/1187916316}
}
Thangavelu, S. A Paley-Wiener theorem for the inverse Fourier transform on some homogeneous spaces. Hiroshima Math. J., Tome 37 (2007) no. 1, pp. 145-159. http://gdmltest.u-ga.fr/item/1187916316/