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

TL;DR

This paper introduces a Fourier-like transform for locally compact abelian groups using cosets of closed subgroups, and analyzes associated wavelet multipliers and Landau-Pollak-Slepian operators, establishing their boundedness, Schatten class membership, and trace properties.

Contribution

It defines a new Fourier-like transform on LCA groups and studies the boundedness and spectral properties of related operators, connecting them to generalized Landau-Pollak-Slepian operators.

Findings

Transform is $L^p$ bounded and in Schatten p-class.

Operators' trace class properties are characterized.

Connection established with generalized Landau-Pollak-Slepian operators.

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.