Microlocal properties of Shubin pseudodifferential and localization operators

TL;DR

This paper studies the microlocal behavior of Shubin pseudodifferential and localization operators, establishing their microlocality and microellipticity within Shubin-type Sobolev spaces.

Contribution

It provides new results on the microlocal regularity, microlocality, and microellipticity of these operators in the context of global analysis.

Findings

Proved microlocality of localization and Shubin pseudodifferential operators.

Established microellipticity properties in Shubin Sobolev spaces.

Analyzed the microlocal regularity in a global setting.

Abstract

We investigate global microlocal properties of localization operators and Shubin pseudodifferential operators. The microlocal regularity is measured in terms of a scale of Shubin-type Sobolev spaces. In particular, we prove microlocality and microellipticity of these operators.