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.

DOI : 10.5802/ambp.201
Minggen, Cui 1 ; Yanying, Zhang 2

1 Harbin Institute of Technology Department of Mathematics No.2 WenHua west road WeiHai, ShanDong, 264209 CHINA
2 Harbin Normal University Department of Information Science HeXing Road Harbin,HeiLongJiang, 150080 CHINA
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Minggen, Cui; Yanying, Zhang. 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. http://www.numdam.org/articles/10.5802/ambp.201/

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

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

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

[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., Volume 66 (2002), p. 149-158(Russian) | MR | Zbl

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

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