Uncertainty principles on certain Lie groups

Sitaram, Alladi; Sundari, M.; Thangavelu, Sundaram

doi:10.1007/bf02880360

Cited by 88 publications

(67 citation statements)

References 12 publications

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“…https://doi.org/10.1017/S1446788700035886 [11] Uncertainty principles like Hardy's theorem on some Lie groups 299…”

Section: Heisenberg Groupsmentioning

confidence: 99%

Uncertainty principles like Hardy's theorem on some Lie groups

Bagchi¹,

Ray²

1998

J Aust Math Soc A

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We extend an uncertainty principle due to Cowling and Price to Euclidean spaces, Heisenberg groups and the Euclidean motion group of the plane. This uncertainty principle is a generalisation of a classical result due to Hardy. We also show that on the real line this uncertainty principle is almost equivalent to Hardy's theorem.1991 Mathematics subject classification (Amer. Math. Soc): primary 22E25, 22E30.

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“…https://doi.org/10.1017/S1446788700035886 [11] Uncertainty principles like Hardy's theorem on some Lie groups 299…”

Section: Heisenberg Groupsmentioning

confidence: 99%

Uncertainty principles like Hardy's theorem on some Lie groups

Bagchi¹,

Ray²

1998

J Aust Math Soc A

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“…One of our motivations comes from a well known result due to G. H. Hardy [16, pp. 131] (see also [1] for a recent survey on this topic), which concerns the decay of a function f and its Fourier transform, f (ξ) = (2π) The corresponding result in terms of L 2 -norms and established in [15] 2 u(x, T ) are in L 2 (R n ) and αβ ≤ 4T , then u ≡ 0.…”

Section: Introductionmentioning

confidence: 99%

Hardy's uncertainty principle, convexity and Schrödinger evolutions

Escauriaza¹,

Kenig²,

Ponce³

et al. 2008

J. Eur. Math. Soc.

164

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“…However, as far as we are aware, until very recently no systematic attempt was made to generalize Hardy's theorem to other Lie groups. In [12], [13], and [15], this result has been generalized to the Heisenberg groups H n , the Euclidean motion groups M (n) and for certain eigenfunction expansions. In this paper we establish an analogue of Hardy's theorem for a class of noncompact semisimple Lie groups and all symmetric spaces of the noncompact type.…”

Section: Introductionmentioning

confidence: 99%