Continuity properties of multilinear localization operators on modulation spaces

TL;DR

This paper introduces multilinear localization operators via the short-time Fourier transform and Weyl pseudodifferential operators, establishing their properties and continuity on modulation spaces, extending linear case results.

Contribution

It provides a new interpretation of multilinear localization operators as Weyl pseudodifferential operators with convolution-based symbols, and studies their continuity on modulation spaces.

Findings

Localization operators are Weyl pseudodifferential operators with convolution symbols.

Continuity properties of multilinear localization operators on modulation spaces are established.

Results extend known linear case properties to multilinear settings.

Abstract

We introduce multilinear localization operators in terms of the short-time Fourier transform, and multilinear Weyl pseudodifferential operators. We prove that such localization operators are in fact Weyl pseudodifferential operators whose symbols are given by the convolution between the symbol of the localization operator and the multilinear Wigner transform. For such interpretation we use the kenrel theorem for the Gelfand-Shilov space. Furthermore, we study the continuity properties of the multilinear localization operators on modulation spaces. Our results extend some known results when restricted to the linear case.