p-adic Dual Shearlet Frames

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 Gp 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 L2(Q^2p). The discrete p-adic shearlet frames for L^2(Q^2p) is discussed. Also we prove that the frame operator S associated with the group Gp of all with the shearlet frame SH(ψ;Λ) is a Fourier multiplier with a function in terms of ψˆ. For a measurable subset H⊂Q^2p, we considered a subspace L^2(H)∨ of L^2(Q2p). Finally we give a necessary condition for two functions in L2(Q^2p) to generate a p-adic dual shearlet tight frame via admissibility.