A theorem due to Hardy states that, if f is a function on R such that \f(x)\ ≤ C e-α\x\2 for all x in R and |f̂(ξ)| ≤ C e-β|ξl2 for all ξ, in R, where α > 0, β > 0, and αβ > 1/4, then f = 0. A version of this celebrated theorem is proved for two classes of Lie groups : two-step nilpotent Lie groups and harmonic NA groups, the latter being a generalisation of noncompact rank-1 symmetric spaces. In the first case the group Fourier transformation is considered; in the second case an analogue of the Helgason-Fourier transformation for symmetric spaces is considered

Astengo, F., Cowling, M., DI BLASIO, B., Sundari, M. (2000). Hardy's uncertainty principle on certain Lie groups. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 62(2), 461-472 [10.1112/S0024610700001186].

Hardy's uncertainty principle on certain Lie groups

DI BLASIO, BIANCA;
2000

Abstract

A theorem due to Hardy states that, if f is a function on R such that \f(x)\ ≤ C e-α\x\2 for all x in R and |f̂(ξ)| ≤ C e-β|ξl2 for all ξ, in R, where α > 0, β > 0, and αβ > 1/4, then f = 0. A version of this celebrated theorem is proved for two classes of Lie groups : two-step nilpotent Lie groups and harmonic NA groups, the latter being a generalisation of noncompact rank-1 symmetric spaces. In the first case the group Fourier transformation is considered; in the second case an analogue of the Helgason-Fourier transformation for symmetric spaces is considered
Articolo in rivista - Articolo scientifico
Lie groups
English
2000
62
2
461
472
none
Astengo, F., Cowling, M., DI BLASIO, B., Sundari, M. (2000). Hardy's uncertainty principle on certain Lie groups. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 62(2), 461-472 [10.1112/S0024610700001186].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/17758
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