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

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dc.creatorRousseau, Jerome Le
dc.date2005-01-07
dc.date.accessioned2026-07-07T05:15:54Z
dc.date.available2026-07-07T05:15:54Z
dc.descriptionAn 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 $\infty$.
dc.descriptiondate de redaction: 2004
dc.identifierhttps://arxiv.org/abs/math/0501101
dc.identifierhttp://arxiv.org/abs/math/0501101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73790
dc.subjectAnalysis of PDEs
dc.subjectAMS 2000: 35L05, 35L80, 35S10, 35S30, 86A15
dc.titleFourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations I: convergence in Sobolev spaces
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