Remarks on semiclassical wavefront set

TL;DR

This paper explores the properties of semiclassical wavefront sets, linking the support of pseudodifferential operator symbols to these sets using coherent states dependent on Planck's constant.

Contribution

It provides a characterization of the essential support of symbols of semiclassical pseudodifferential operators via semiclassical wavefront sets, employing a novel proof technique.

Findings

Characterization of symbol support using wavefront sets

Use of phase space-dependent coherent states in proofs

Enhanced understanding of semiclassical pseudodifferential operators

Abstract

The essential support of the symbol of a semiclassical pseudodifferentail operator is characterized by semiclassical wavefront sets of distributions. The proof employs a coherent state whose center in phase space is dependent on Planck's constant.