On traces of Fourier integral operators on submanifolds (Q1731496)

Given an operator \(A\) on a manifold \(M\), \textit{S. P. Novikov} and \textit{B. Yu. Sternin} [Sov. Math., Dokl. 7, 1373--1376 (1966; Zbl 0174.41302); translation from Dokl. Akad. Nauk SSSR 170, 1265--1268 (1966)] defined traces of \(A\) on arbitrary submanifolds in \(M\). These traces are operators on submanifolds. The aim of this paper is to study traces of Fourier integral operators (FIO). The author defines the notion of trace for Lagrangian submanifolds, and his main theorem describes sufficient conditions under which the trace of a FIO is associated with the trace of the corresponding Lagrangian manifolds. Moreover, explicit formulas for amplitudes of traces are given.