Compactness of localization operators on modulation spaces of $\omega$-tempered distributions

TL;DR

This paper establishes conditions under which localization operators are compact on certain modulation spaces of -tempered distributions, expanding understanding of their functional analysis properties.

Contribution

It provides new sufficient conditions for the compactness of localization operators on weighted modulation spaces of -tempered distributions.

Findings

Derived sufficient conditions for compactness.

Extended analysis to modulation spaces with exponential weights.

Enhanced understanding of localization operators in time-frequency analysis.

Abstract

We give sufficient conditions for compactness of localization operators on modulation spaces $\textbf{M}^{p,q}_{m_{\lambda}}( \mathbb{R}^{d})$ of $\omega$-tempered distributions whose short-time Fourier transform is in the weighted mixed space $L^{p,q}_{m_\lambda}$ for $m_\lambda(x)=e^{\lambda\omega(x)}$.