Uncertainty principle for vector-valued functions
The uncertainty principle for vector-valued functions of $ L^2({\mathbb{R}}^n, {\mathbb{R}}^m) $ with $ n\ge 2 $ are studied. We provide a stronger uncertainty principle than the existing one in literature when $ m\ge 2 $. The phase and the amplitude derivatives in the sense of the Fourier transform...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-04-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024611?viewType=HTML |
| Summary: | The uncertainty principle for vector-valued functions of $ L^2({\mathbb{R}}^n, {\mathbb{R}}^m) $ with $ n\ge 2 $ are studied. We provide a stronger uncertainty principle than the existing one in literature when $ m\ge 2 $. The phase and the amplitude derivatives in the sense of the Fourier transform are considered when $ m = 1 $. Based on these definitions, a generalized uncertainty principle is given. |
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| ISSN: | 2473-6988 |