A normal form around a Lagrangian submanifold of radial points

Abstract

In this work we produce microlocal normal forms for pseudodifferential operators which have a Lagrangian submanifold of radial points. This answers natural questions about such operators and their associated classical dynamics. In a sequel, we will give a microlocal parametrix construction, as well as a construction of a microlocal Poisson operator, for such pseudodifferential operators.