Uncertainty principle for vector-valued functions

Feifei Qu; Xin Wei; Juan Chen; Feifei Qu; Xin Wei; Juan Chen

doi:10.3934/math.2024611

AIMS Mathematics

2024, Volume 9, Issue 5: 12494-12510. doi: 10.3934/math.2024611

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Research article

Uncertainty principle for vector-valued functions

1.
School of Science, Tianjin University of Technology and Education, Tianjin, 300222, China
2.
School of Science, Xi'an Shiyou University, Xi'an, 710065, China
3.
Tianjin Sino-german University of Applied Sciences, Tianjin, 300350, China

Received: 04 January 2024 Revised: 08 March 2024 Accepted: 15 March 2024 Published: 01 April 2024
MSC : 42B10, 94A12

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.
- uncertainty principle,
- vector-valued functions,
- Fourier derivative
Citation: Feifei Qu, Xin Wei, Juan Chen. Uncertainty principle for vector-valued functions[J]. AIMS Mathematics, 2024, 9(5): 12494-12510. doi: 10.3934/math.2024611

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Abstract

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.

References

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