Generalized oscillatory integrals and Fourier integral operators

DOI10.1017/S0013091506000915zbMath1181.35360arXivmath/0607706MaRDI QIDQ3633291

Claudia Garetto, Günther Hörmann, Michael Oberguggenberger

Publication date: 18 June 2009

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607706

zbMATH Keywords

Fourier integral operatorsmicrolocal analysisalgebras of generalized functions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Fourier integral operators applied to PDEs (35S30) Pseudodifferential operators (47G30)

Related Items (10)

Nonlinear generalized sections of vector bundles ⋮ Propagation of singularities for generalized solutions to nonlinear wave equations ⋮ Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory ⋮ The Wave Equation with a Discontinuous Coefficient Depending on Time Only: Generalized Solutions and Propagation of Singularities ⋮ Symplectic Modules Over Colombeau-Generalized Numbers ⋮ Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities ⋮ Inversion of Colombeau generalized functions ⋮ Generalized Fourier Integral Operators on Spaces of Colombeau Type ⋮ On Local and Global Regularity of Fourier Integral Operators ⋮ Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations

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