On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

DOI10.2298/BMAT0631115GzbMath1121.46037arXivmath/0507222OpenAlexW2050789040MaRDI QIDQ5424638

Publication date: 5 November 2007

Published in: Bulletin: Classe des sciences mathematiques et natturalles (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507222

Mathematics Subject Classification ID

Duality theory for topological vector spaces (46A20) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Pseudodifferential operators (47G30)

Related Items (10)

Nonlinear generalized sections of vector bundles ⋮ Propagation of singularities for generalized solutions to nonlinear wave equations ⋮ A Convenient Notion of Compact Set for Generalized Functions ⋮ 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 ⋮ Hyperbolic Systems with Discontinuous Coefficients: Generalized Wavefront Sets ⋮ Generalized Fourier Integral Operators on Spaces of Colombeau Type ⋮ Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations ⋮ Microlocal analysis of generalized pullbacks of Colombeau functions ⋮ Closed graph and open mapping theorems for topological $ \tilde \lc $-modules and applications

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