The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field
Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 1, p. 181-193

In this paper, two important geometric concepts–grapical center and width, are introduced in $p$-adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in $p$-adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on $p$-adic numbers field.

@article{AMBP_2005__12_1_181_0,
author = {Minggen, Cui and Yanying, Zhang},
title = {The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field},
journal = {Annales math\'ematiques Blaise Pascal},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {12},
number = {1},
year = {2005},
pages = {181-193},
doi = {10.5802/ambp.201},
mrnumber = {2126447},
zbl = {02215256},
language = {en},
url = {http://www.numdam.org/item/AMBP_2005__12_1_181_0}
}

Minggen, Cui; Yanying, Zhang. The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field. Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 1, pp. 181-193. doi : 10.5802/ambp.201. http://www.numdam.org/item/AMBP_2005__12_1_181_0/

[1] Cui, M. G.; Yao, H.M; Liu, H.P The Affine Frame In $p$-adic Analysis, Annales Mathematiques Blaise Pascal, Tome 10 (2003), pp. 297-303 | Article | Numdam | MR 2031273 | Zbl 1066.42501

[2] Cui, M. G. On the Wavelet Transform in the field ${ℚ}_{p}$ of p-adic numbers, Appl. Comput. Harmonic Analysis, Tome 13 (2002), pp. 162-168 | Article | MR 1942750 | Zbl 1022.42025

[3] Gao, G.H; Cui, M.G Calculus on the field ${ℚ}_{p}$ of $p$-adic numbers, J. of Natural Science of Heilongjiang University, Tome 3 (2003), p. 15-16 | Zbl 1053.26019

[4] Halmos, Paul R. Measure Theory, Beijing Scientific Publishing House(Chinese Translation), Beijing (1965)

[5] Kozyrev, S. V. Wavelet theory as $p$-adic apectral analysis, Izv. Russ, Akad. Nauk, Ser. Math., Tome 66 (2002), p. 149-158(Russian) | MR 1918846 | Zbl 1016.42025

[6] Vladimirov, V.S; Volovich, I.V; Zelenov, E.I p-adic Analysis and Mathematical Physics, Internat. Math. Res. Notices, Tome 13 (2996), p. 6613-663 | Zbl 0864.46048 | Zbl 0812.46076