Microlocal Projectors

TL;DR

This paper investigates operators resembling Bergman kernels, revealing their deep geometric connections and showing they can be locally conjugated, thus advancing understanding of approximate projectors in complex analysis.

Contribution

It introduces a framework linking approximate projectors to geometric data and demonstrates their local conjugation properties.

Findings

Operators share key features with Bergman kernels.

Such operators are associated with rich geometric data.

All such operators can be locally conjugated.

Abstract

The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on the one hand, and that on the other hand, all such operators can be locally conjugated in some sense.