$p$-adic Dual Shearlet Frames

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 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 L ( Qp ) . The discrete p-adic shearlet frames for L ( Qp ) 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 ψ̂. For a measurable subset H ⊂ Qp, we considered a subspace L (H) of L ( Qp ) . Finally we give a necessary condition for two functions in L ( Qp ) to generate a p-adic dual shearlet tight frame via admissibility.