TY - JOUR
ID - 34965
TI - $p$-adic Dual Shearlet Frames
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Fatemidokht, Mahdieh
AU - Askari Hemmat, Ataollah
AD - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
AD - Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Y1 - 2019
PY - 2019
VL - 16
IS - 1
SP - 47
EP - 56
KW - $p$-adic numbers
KW - Dual frame
KW - $p$-adic shearlet system
KW - $p$-adic dual tight frame
DO - 10.22130/scma.2018.77684.355
N2 - 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.
UR - http://scma.maragheh.ac.ir/article_34965.html
L1 - http://scma.maragheh.ac.ir/article_34965_b1db50eb43891d7297fa1e8dc1a5b630.pdf
ER -