On traces of Fourier integral operators on submanifolds
Given a smooth embedding $i\colon X \hookrightarrow M$ of manifolds and a Fourier integral operator $Φ= Φ(Λ)$ on $M$ associated with a Lagrangian submanifold $Λ\subset T^*(X\times X) \setminus \{0\}$, we consider its trace $i^!(Λ)$ on the submanifold $X$, i.e. the composition $i^* Φi_*$, where $i^*$ and $i_*$ are the boundary and coboundary operators, respectively. We establish the conditions under which the trace $i^!(Φ)$ is also a Fourier integral operator and calculate its amplitude in canonical local coordinates.
math.AP↗