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Research Article | Open Access

Uncertainty principle for vector-valued functions

Feifei Qu1, Xin Wei2( ), Juan Chen3
School of Science, Tianjin University of Technology and Education, Tianjin, 300222, China
School of Science, Xi'an Shiyou University, Xi'an, 710065, China
Tianjin Sino-german University of Applied Sciences, Tianjin, 300350, China
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Abstract

The uncertainty principle for vector-valued functions of L 2 ( R n , R m ) with n ≥ 2 are studied. We provide a stronger uncertainty principle than the existing one in literature when m ≥ 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.

Keywords

uncertainty principlevector-valued functionsFourier derivative
CLC number: 42B10, 94A12

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 12494-12510
DOI: 10.3934/math.2024611

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Cite this article:
Qu F, Wei X, Chen J. Uncertainty principle for vector-valued functions. AIMS Mathematics, 2024, 9(5): 12494-12510. https://doi.org/10.3934/math.2024611

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Received: 04 January 2024
Revised: 08 March 2024
Accepted: 15 March 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)