Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-\(H\)-translation-invariant functions

Abstract

By using a coset of closed subgroup, we define a Fourier like transform for locally compact abelian (LCA) topological groups. We studied two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian topological groups associated to the transform and show that the transforms are \(L^p\)bounded linear operators, and are in Schatten p-class for \(1\leq p\leq \infty\). Finally, we determine their trace class and also obtain a connection with the generalized Landau-Pollak-Slepian operators.