Weyl-Heisenberg frame in $p$-adic analysis
Annales Mathématiques Blaise Pascal, Tome 12 (2005) no. 1, pp. 195-203.

In this paper, we establish an one-to-one mapping between complex-valued functions defined on ${R}^{+}\cup \left\{0\right\}$ 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.

@article{AMBP_2005__12_1_195_0,
author = {Minggen Cui and Xueqin Lv},
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},
mrnumber = {2126448},
zbl = {02215257},
language = {en},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.202/}
}
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/

[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 | Article | MR 1942750 | Zbl 1022.42025

[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 02215256

[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) | Article | Numdam | MR 2031273 | Zbl 1066.42501

[4] S.V Kozyrev Wavelet theory as p-adic spectral analysis, Izv.Russ.Akad.Nauk,Ser, Volume 2 (2002), pp. 149-158 | MR 1918846 | Zbl 1016.42025

[5] V. S. Vladimirov; I. V. Volovich; E. I. Zelenov $p$-adic Analysis and Mathematical Physics, World Scientific, 1994 | MR 1288093 | Zbl 0812.46076

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