On the Solvability of Pseudodifferential Equations in Microdistributions

The chapter describes a microlocal parametrix for a pseudodifferential operator of principal type \(P(x,D)\) satisfying Condition \((\Psi )\) . The parametrix is represented by a Fourier Integral Operator with a complex phase-function \(\varphi \) of the FBI type, and Condition \(( \Psi )\) is equated to the quasiconvexity of the trace of the imaginary part of \(\varphi \) on special curves intersecting the characteristic set of \(P(x,D)\) .