A complete analogue of Hardy's theorem on semisimple Lie groups

Rudra P. Sarkar. "A complete analogue of Hardy's theorem on semisimple Lie groups." Colloquium Mathematicae 93.1 (2002): 27-40. <http://eudml.org/doc/284582>.

@article{RudraP2002,
abstract = {A result by G. H. Hardy ([11]) says that if f and its Fourier transform f̂ are $O(|x|^m e^\{-αx²\})$ and $O(|x|ⁿ e^\{-x²/(4α)\})$ respectively for some m,n ≥ 0 and α > 0, then f and f̂ are $P(x)e^\{-αx²\}$ and $P^\{\prime \}(x)e^\{-x²/(4α)\}$ respectively for some polynomials P and P’. If in particular f is as above, but f̂ is $o(e^\{-x²/(4α)\})$, then f = 0. In this article we will prove a complete analogue of this result for connected noncompact semisimple Lie groups with finite center. Our proof can be carried over to the real reductive groups of the Harish-Chandra class.},
author = {Rudra P. Sarkar},
journal = {Colloquium Mathematicae},
keywords = {Hardy's theorem; uncertainty principle; semisimple Lie groups},
language = {eng},
number = {1},
pages = {27-40},
title = {A complete analogue of Hardy's theorem on semisimple Lie groups},
url = {http://eudml.org/doc/284582},
volume = {93},
year = {2002},
}

TY - JOUR
AU - Rudra P. Sarkar
TI - A complete analogue of Hardy's theorem on semisimple Lie groups
JO - Colloquium Mathematicae
PY - 2002
VL - 93
IS - 1
SP - 27
EP - 40
AB - A result by G. H. Hardy ([11]) says that if f and its Fourier transform f̂ are $O(|x|^m e^{-αx²})$ and $O(|x|ⁿ e^{-x²/(4α)})$ respectively for some m,n ≥ 0 and α > 0, then f and f̂ are $P(x)e^{-αx²}$ and $P^{\prime }(x)e^{-x²/(4α)}$ respectively for some polynomials P and P’. If in particular f is as above, but f̂ is $o(e^{-x²/(4α)})$, then f = 0. In this article we will prove a complete analogue of this result for connected noncompact semisimple Lie groups with finite center. Our proof can be carried over to the real reductive groups of the Harish-Chandra class.
LA - eng
KW - Hardy's theorem; uncertainty principle; semisimple Lie groups
UR - http://eudml.org/doc/284582
ER -