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

Cui Minggen; Zhang Yanying

doi:10.5802/ambp.201

The Heisenberg uncertainty relation in harmonic analysis on

p

-adic numbers field

Cui Minggen ¹ ; Zhang Yanying 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

DOI : 10.5802/ambp.201

Affiliations des auteurs :

Cui Minggen ¹ ; Zhang Yanying 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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     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},
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     number = {1},
     year = {2005},
     doi = {10.5802/ambp.201},
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     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.201/}
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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/

Bibliographie
Cité par

[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 | DOI | EuDML | Numdam | MR | Zbl

[2] M. G. Cui 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] G.H Gao; M.G Cui 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] 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 | Zbl

[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

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