Pseudo-differential operators in algebras of generalized functions and global hypoellipticity
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Publication:1431626
DOI10.1023/B:ACAP.0000013814.89972.3CzbMath1060.46029arXivmath/0502283OpenAlexW2004856293MaRDI QIDQ1431626
Publication date: 11 June 2004
Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0502283
Hypoelliptic equations (35H10) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Pseudodifferential operators (47G30)
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Composition and exponential of compactly supported generalized integral operators ⋮ Notes on regularity results in Colombeau algebras ⋮ Divergent type quasilinear Dirichlet problem with singularities ⋮ Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity ⋮ Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory ⋮ Generalized integral operators and Schwartz kernel type theorems ⋮ Generalized Fourier Integral Operators on Spaces of Colombeau Type ⋮ Pointwise characterizations in generalized function algebras ⋮ Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients ⋮ Closed graph and open mapping theorems for topological $ \tilde \lc $-modules and applications ⋮ First-order hyperbolic pseudodifferential equations with generalized symbols ⋮ Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory ⋮ Topological structures in Colombeau algebras: Investigation of the duals of \(\mathcal G_c(\Omega)\), \(\mathcal G(\Omega)\) and \(\mathcal G_{\mathcal S}(\mathbb R^n)\)
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