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

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Sarkar R.

Colloquium Mathematicum

2002

tom 93

nr 1

27-40

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 $P'(x)e^{-x²/(4α)}$ 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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Sarkar R.

1 2002

Wyniki wyszukiwania

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