We find the minimal real number $k$ such that the $k$th power of
the Fourier transform of any continuous, orbital measure on a
classical, compact Lie group belongs to $l^{2}$. This results from
an investigation of the pointwise behaviour of characters on these
groups. An application is given to the study of $L^{p}$-improving
measures.
Publié le : 2004-06-14
Classification:
orbital measures,
compact Lie group,
characters,
43A80,
22E46,
43A65
@article{1087482025,
author = {Hare, Kathryn E. and Yee, Wai Ling},
title = {The Singularity of Orbital Measures on Compact Lie Groups},
journal = {Rev. Mat. Iberoamericana},
volume = {20},
number = {1},
year = {2004},
pages = { 517-530},
language = {en},
url = {http://dml.mathdoc.fr/item/1087482025}
}
Hare, Kathryn E.; Yee, Wai Ling. The Singularity of Orbital Measures on Compact Lie Groups. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp. 517-530. http://gdmltest.u-ga.fr/item/1087482025/