Fourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations II: Microlocal analysis

AbstractAn approximation Ansatz for the solution operator, U(z′,z), of a hyperbolic first-order pseudodifferential equation, ∂z+a(z,x,Dx) with Re(a)⩾0, is constructed as the composition of global Fourier integral operators with complex phases. We investigate the propagation of singularities for this Ansatz and prove microlocal convergence: the wavefront set of the approximated solution is shown to converge to that of the exact solution away from the region where the phase is complex