Microlocal analysis of Colombeau's generalized functions: Propagation of singularities

DOI10.1007/BF02788691zbMath0922.46036OpenAlexW2025035665MaRDI QIDQ1271292

N. Dapić, Stevan Pilipović, Dimitris Scarpalézos

Publication date: 20 October 1999

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02788691

zbMATH Keywords

pointwise regularityColombeau's generalized functionslinear generalized partial differential operatorpointwise wave front

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) General theory of partial differential operators (47F05) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Pseudodifferential operators (47G30)

Related Items (14)

Notes on regularity results in Colombeau algebras ⋮ Microlocal analysis in generalized function algebras based on generalized points and generalized directions ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ Optimal embeddings of ultradistributions into differential algebras ⋮ Regularity, local and microlocal analysis in theories of generalized functions ⋮ Optimal regularization processes on complete Riemannian manifolds ⋮ An Application of Internal Objects to Microlocal Analysis in Generalized Function Algebras ⋮ Topological properties of regular generalized function algebras ⋮ Orthogonal polynomial eigenfunctions of second-order partial differerential equations ⋮ Microlocal properties of basic operations in Colombeau algebras ⋮ Pointwise characterizations in generalized function algebras ⋮ Microlocal analysis of generalized pullbacks of Colombeau functions ⋮ Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients ⋮ Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory

Cites Work

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• Microlocal analysis of Colombeau's generalized functions on a manifold
• Fundamental structures and asymptotic microlocalization in sheaves of generalized functions
• Some remarks on functoriality of Colombeau's construction; topological and microlocal aspects and applications
• Characterization of colombeau generalized functions by their pointvalues
• Hypoelliptic differential operators with generalized constant coefficients

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