The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field

Minggen, Cui; Yanying, Zhang

doi:10.5802/ambp.201

The Heisenberg uncertainty relation in harmonic analysis on

p

-adic numbers field

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

Annales mathématiques Blaise Pascal, Tome 12 (2005) no. 1, pp. 181-193.

Résumé

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/ambp.201

Affiliations des auteurs :

Minggen, Cui ¹ ; Yanying, Zhang ²

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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://archive.numdam.org/articles/10.5802/ambp.201/

Bibliographie
Cité par

[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 $ℚ_{p}$ 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 $ℚ_{p}$ 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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