The Heisenberg uncertainty relation in harmonic analysis on p-adic numbers field
Annales Mathématiques Blaise Pascal, Tome 12 (2005) no. 1, pp. 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 = {Cui Minggen and Zhang Yanying},
     title = {The {Heisenberg} uncertainty relation in harmonic analysis on $p$-adic numbers field},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {181--193},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     number = {1},
     year = {2005},
     doi = {10.5802/ambp.201},
     mrnumber = {2126447},
     zbl = {02215256},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.201/}
}
Cui Minggen; Zhang Yanying. The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field. Annales Mathématiques Blaise Pascal, Tome 12 (2005) no. 1, pp. 181-193. doi : 10.5802/ambp.201. https://ambp.centre-mersenne.org/articles/10.5802/ambp.201/

[1] M. G. Cui; H.M Yao; H.P Liu The Affine Frame In p-adic Analysis, Annales Mathematiques Blaise Pascal, Volume 10 (2003), pp. 297-303 | Article | EuDML 10491 | Numdam | MR 2031273 | Zbl 1066.42501

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

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

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

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

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

Cité par document(s). Sources :