@article {
author = {Fatemidokht, Mahdieh and Askari Hemmat, Ataollah},
title = {$p$-adic Dual Shearlet Frames},
journal = {Sahand Communications in Mathematical Analysis},
volume = {16},
number = {1},
pages = {47-56},
year = {2019},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.77684.355},
abstract = {We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2\left(Q_p^{2}\right)$. The discrete $p$-adic shearlet frames for $L^2\left(Q_p^{2}\right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SH\left( \psi; \Lambda\right)$ is a Fourier multiplier with a function in terms of $\widehat{\psi}$. For a measurable subset $H \subset Q_p^{2}$, we considered a subspace $L^2\left(H\right)^{\vee}$ of $L^2\left(Q_p^{2}\right)$. Finally we give a necessary condition for two functions in $L^2\left(Q_p^{2}\right)$ to generate a p-adic dual shearlet tight frame via admissibility.},
keywords = {$p$-adic numbers,Dual frame,$p$-adic shearlet system,$p$-adic dual tight frame},
url = {https://scma.maragheh.ac.ir/article_34965.html},
eprint = {https://scma.maragheh.ac.ir/article_34965_b1db50eb43891d7297fa1e8dc1a5b630.pdf}
}