%0 Journal Article %T $p$-adic Dual Shearlet Frames %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Fatemidokht, Mahdieh %A Askari Hemmat, Ataollah %D 2019 %\ 10/01/2019 %V 16 %N 1 %P 47-56 %! $p$-adic Dual Shearlet Frames %K $p$-adic numbers %K Dual frame %K $p$-adic shearlet system %K $p$-adic dual tight frame %R 10.22130/scma.2018.77684.355 %X 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. %U https://scma.maragheh.ac.ir/article_34965_b1db50eb43891d7297fa1e8dc1a5b630.pdf