Microlocal Properties of Bisingular Operators

TL;DR

This paper investigates the microlocal behavior of bisingular operators on product manifolds, introducing a wave front set concept and comparing it with the existing $SG$ wave front set to understand their similarities.

Contribution

It defines a new wave front set for bisingular operators and analyzes its properties, providing insights into their microlocal structure and relation to $SG$ wave front sets.

Findings

Introduces a wave front set for bisingular operators

Establishes properties of the new wave front set

Compares with the $SG$ wave front set revealing formal similarities

Abstract

We study the microlocal properties of bisingular operators, a class of operators on the product of two compact manifolds. We define a wave front set for such operators, and analyse its properties. We compare our wave front set with the $SG$ wave front set, a global wave front set which shares with it formal similarities.