%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
%\ 04/24/2019
%V
%N
%P -
%! $p$-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 $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for $L^2left(Q_p^{2}right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SHleft( psi; Lambdaright)$ 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 $L^2left(Hright)^{vee}$ of $L^2left(Q_p^{2}right)$. Finally we give a necessary condition for two functions in $L^2left(Q_p^{2}right)$ to generate a p-adic dual shearlet tight frame via admissibility.
%U