Geodesic
A simple observation on Heisenberg-like uncertainty principles
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 113-120

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A solution is given to a conjecture proposed recently by Y. Wigderson and A. Wigderson concerning a “Heisenberg-like” uncertainty principle. That conjecture is about the image of the map $ f \mapsto \frac{\|f\|_q\|\hat{f}\|_q}{\|f\|_2\|\hat{f}\|_2}, f\in \mathscr{S}(\mathbb{R})\setminus\{0\} $, where $\mathscr{S}(\mathbb{R}) $ stands for the Schwartz class of functions on the real line. Also, a more general question is answered, where the $L_2$ norm is replaced by the $L_p$ norm in the denominator. 
@article{ZNSL_2021_503_a6,
     author = {Yiyu Tang},
     title = {A simple observation on {Heisenberg-like} uncertainty principles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--120},
     publisher = {mathdoc},
     volume = {503},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a6/}
}
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Yiyu Tang. A simple observation on Heisenberg-like uncertainty principles. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 113-120. http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a6/