Fourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations I: convergence in Sobolev spaces

Jerome Le Rousseau

An approximation Ansatz for the operator solution, $U(z^{\prime },z)$, of a hyperbolic first-order pseudodifferential equation, $\d_z + a(z,x,D_x)$ with $\Re (a)\ge 0$, is constructed as…