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

Rudra P. Sarkar

Rudra P. Sarkar

Colloquium Mathematicae, Tome 91 (2002), p. 27-40 / Harvested from The Polish Digital Mathematics Library

Résumé

A result by G. H. Hardy ([11]) says that if f and its Fourier transform f̂ are $O (| x |^{m} e^{- α x ²})$ and $O (| x | ⁿ e^{- x ² / (4 α)})$ respectively for some m,n ≥ 0 and α > 0, then f and f̂ are $P (x) e^{- α x ²}$ and $P^{'} (x) e^{- x ² / (4 α)}$ respectively for some polynomials P and P’. If in particular f is as above, but f̂ is $o (e^{- x ² / (4 α)})$ , 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.

Publié le : 2002-01-01

Zbl 1011.43004

EUDML-ID : urn:eudml:doc:284582

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Rudra P. Sarkar. A complete analogue of Hardy's theorem on semisimple Lie groups. Colloquium Mathematicae, Tome 91 (2002) pp. 27-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-4/