Action of micro-differential operators on quantized contact transformations

TL;DR

This paper proves that quantized contact transforms commute with microdifferential operators, filling a gap in the literature, and applies this to the microlocal Radon transform.

Contribution

It provides a complete proof of the commutation between QCT and microdifferential operators, which was previously unestablished.

Findings

QCT commute with microdifferential operators

Complete proof provided for this commutation

Application to microlocal Radon transform

Abstract

Quantized contact transforms (QCT) have been constructed in \cite{SKK73}. We give here a complete proof of the fact that such QCT commute with the action of microdifferential operators. To our knowledge, such a proof did not exist in the literature. We apply this result to the microlocal Radon transform.