Weyl-Heisenberg frame in $p$-adic analysis

Minggen Cui; Xueqin Lv

doi:10.5802/ambp.202

Weyl-Heisenberg frame in

p

-adic analysis

Minggen Cui ¹ ; Xueqin Lv ²

¹ Harbin Institute of Technology Department of Mathematics WEN HUA XI ROAD WEIHAI Shan Dong, 264209 P.R.China
² Harbin Normal University Department of Information Science HE XING ROAD Harbin HeiLongJiang, 150001 P.R.China

Annales mathématiques Blaise Pascal, Tome 12 (2005) no. 1, pp. 195-203.

Résumé

In this paper, we establish an one-to-one mapping between complex-valued functions defined on $R^{+} \cup {0}$ and complex-valued functions defined on $p$ -adic number field $Q_{p}$ , and introduce the definition and method of Weyl-Heisenberg frame on hormonic analysis to $p$ -adic anylysis.

MR Zbl

DOI : 10.5802/ambp.202

Affiliations des auteurs :

Minggen Cui ¹ ; Xueqin Lv ²

¹ Harbin Institute of Technology Department of Mathematics WEN HUA XI ROAD WEIHAI Shan Dong, 264209 P.R.China
² Harbin Normal University Department of Information Science HE XING ROAD Harbin HeiLongJiang, 150001 P.R.China

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     title = {Weyl-Heisenberg frame in $p$-adic analysis},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {195--203},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     number = {1},
     year = {2005},
     doi = {10.5802/ambp.202},
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     zbl = {02215257},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.202/}
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Minggen Cui; Xueqin Lv. Weyl-Heisenberg frame in $p$-adic analysis. Annales mathématiques Blaise Pascal, Tome 12 (2005) no. 1, pp. 195-203. doi : 10.5802/ambp.202. https://ambp.centre-mersenne.org/articles/10.5802/ambp.202/

Bibliographie
Cité par

[1] MingGen Cui; GuangHong Gao On the wavelet transform in the field $ℚ_{p}$ of p-adic Numbers, Applied and Computational Hormonic Analysis, Volume 13 (2002), pp. 162-168 | DOI | MR | Zbl

[2] MingGen Cui; YanYing Zhang The Heisenberg Uncertainty Relation In Harmonic Analysis On p-adic Numbers Field (Dans ce fascicule des Annales Mathématiques Blaise Pascal) | Numdam | Zbl

[3] HuanMin Yao MingGen Cui; HuanPing Liu The Affine Frame In $p$ -adic Analysis, Annales Mathématiques Blaise Pascal, Volume 10 (2003), pp. 297-303 (math.66) | DOI | Numdam | MR | Zbl

[4] S.V Kozyrev Wavelet theory as p-adic spectral analysis, Izv.Russ.Akad.Nauk,Ser, Volume 2 (2002), pp. 149-158 | MR | Zbl

[5] V. S. Vladimirov; I. V. Volovich; E. I. Zelenov $p$ -adic Analysis and Mathematical Physics, World Scientific, 1994 | MR | Zbl

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