On Lorentz geometry in algebras of generalized functions

DOI10.1017/S0308210506000898zbMath1168.46024arXivmath-ph/0604052OpenAlexW1987891081MaRDI QIDQ3521224

Eberhard Mayerhofer

Publication date: 21 August 2008

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0604052

zbMATH Keywords

causalitydominant energy conditionColombeau algebrasalgebras of generalized functionsLorentz geometry

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

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The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data ⋮ Inverse Function Theorems for Generalized Smooth Functions ⋮ A Convenient Notion of Compact Set for Generalized Functions ⋮ Symmetric hyperbolic systems in algebras of generalized functions and distributional limits ⋮ Foundations of the calculus of variations in generalized function algebras ⋮ Wave Equations and Symmetric First-order Systems in Case of Low Regularity ⋮ Symplectic Modules Over Colombeau-Generalized Numbers ⋮ The wave equation on singular space-times ⋮ Wave-type equations of low regularity ⋮ Algebras of generalized functions with smooth parameter dependence

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