An approximation Ansatz for the operator solution, 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. The symbol a(z, ·) is assumed to have a regularity as low as Holder, C 0,α , with respect to the evolution parameter z. We 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 ∞, with a convergence of order α. We also study the consequences of some truncation approximations of the symbol a(z, · )i n the construction of the Ansatz.
['Jérôme Le Rousseau']
On the convergence of some products of Fourier integral operators