HARDY'S THEOREM FOR GABOR TRANSFORM

被引：3

作者：

Bansal, Ashish ^{[1
]}

Kumar, Ajay ^{[2
]}

Sharma, Jyoti ^{[2
]}

机构：

[1] Univ Delhi, Keshav Mahavidyalaya, Dept Math, H-4-5 Zone, Delhi 110034, India

[2] Univ Delhi, Dept Math, Delhi 110007, India

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2019年 / 106卷 / 02期

关键词：

Hardy's theorem; Fourier transform; continuous Gabor transform; nilpotent Lie group; UNCERTAINTY PRINCIPLES;

D O I：

10.1017/S1446788718000204

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Hardy's uncertainty principle for the Gabor transform is proved for locally compact abelian groups having noncompact identity component and groups of the form R-n x K, where K is a compact group having irreducible representations of bounded dimension. We also show that Hardy's theorem fails for a connected nilpotent Lie group G which admits a square integrable irreducible representation. Further, a similar conclusion is made for groups of the form G x D, where D is a discrete group.

引用

页码：143 / 159

页数：17

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