An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups (Q1365255)
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scientific article; zbMATH DE number 1054235
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups |
scientific article; zbMATH DE number 1054235 |
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An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups (English)
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1 February 1998
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The main result is a generalization of a theorem of Hardy saying that a function on the real line and its Fourier transform cannot both be ``very rapidly decreasing'' to all noncompact semisimple Lie groups with finite center and one conjugacy class of Cartan subgroups. The result is also extended to \(\text{SL}(2,R)\) and to symmetric spaces of noncompact type. Such results can be viewed as uncertainty principles.
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Fourier transforms of rapidly decreasing functions on semisimple Lie groups
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