2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73790An approximation Ansatz for the operator solution, $U(z',z)$, of a hyperbolic first-order pseudodifferential equation, $\d_z + a(z,x,D_x)$ with $\Re (a) \geq 0$, is constructed as the composition of global Fourier integral operators with complex phases. An estimate of the operator norm in $L(H^{(s)},H^{(s)})$ of these operators is provided which allows to prove a convergence result for the Ansatz to $U(z',z)$ in some Sobolev space as the number of operators in the composition goes to $\infty$.date de redaction: 2004Analysis of PDEsAMS 2000: 35L05, 35L80, 35S10, 35S30, 86A15text