Fourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations I: convergence in Sobolev spaces
نویسنده
چکیده
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. An estimate of the operator norm in L(H, H) 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 ∞. AMS 2000 subject classification: 35L05, 35L80, 35S10, 35S30, 86A15.
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