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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-04-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024611?viewType=HTML |
| _version_ | 1797206071676239872 |
|---|---|
| author | Feifei Qu Xin Wei Juan Chen |
| author_facet | Feifei Qu Xin Wei Juan Chen |
| author_sort | Feifei Qu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T09:01:11Z |
| format | Article |
| id | doaj.art-ced7453520d144cc9ae9e489ff3dfa82 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T09:01:11Z |
| publishDate | 2024-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ced7453520d144cc9ae9e489ff3dfa822024-04-16T01:26:39ZengAIMS PressAIMS Mathematics2473-69882024-04-0195124941251010.3934/math.2024611Uncertainty principle for vector-valued functionsFeifei Qu0Xin Wei1Juan Chen 21. School of Science, Tianjin University of Technology and Education, Tianjin, 300222, China2. School of Science, Xi'an Shiyou University, Xi'an, 710065, China3. Tianjin Sino-german University of Applied Sciences, Tianjin, 300350, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/math.2024611?viewType=HTMLuncertainty principlevector-valued functionsfourier derivative |
| spellingShingle | Feifei Qu Xin Wei Juan Chen Uncertainty principle for vector-valued functions AIMS Mathematics uncertainty principle vector-valued functions fourier derivative |
| title | Uncertainty principle for vector-valued functions |
| title_full | Uncertainty principle for vector-valued functions |
| title_fullStr | Uncertainty principle for vector-valued functions |
| title_full_unstemmed | Uncertainty principle for vector-valued functions |
| title_short | Uncertainty principle for vector-valued functions |
| title_sort | uncertainty principle for vector valued functions |
| topic | uncertainty principle vector-valued functions fourier derivative |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024611?viewType=HTML |
| work_keys_str_mv | AT feifeiqu uncertaintyprincipleforvectorvaluedfunctions AT xinwei uncertaintyprincipleforvectorvaluedfunctions AT juanchen uncertaintyprincipleforvectorvaluedfunctions |