Grosser, Michael; Farkas, Eva; Kunzinger, Michael; Steinbauer, Roland On the foundations of nonlinear generalized functions. I, II. (English) Zbl 0985.46026 Mem. Am. Math. Soc. 729, xi, 93 p. (2001). A diffeomorphism-invariant differential algebra of generalized functions of Colombeau type \({\mathcal G}^d(\Omega)\) is constructed with a canonical copy of the sapce of Schwartz distributions \({\mathcal D}'(\Omega)\). The result is important for the nonlinear theory of generalized functions and for functional analysis in general. It opens the door to applications to differential geometry, partial differential equations with origin in geometry, and relativity theory. Reviewer: Todor D.Todorov (San Luis Obispo) Cited in 2 ReviewsCited in 25 Documents MSC: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 26E15 Calculus of functions on infinite-dimensional spaces 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces 35D05 Existence of generalized solutions of PDE (MSC2000) 35L70 Second-order nonlinear hyperbolic equations Keywords:Colombeau algebra; diffeomorphism-invariant differential algebra of generalized functions of Colombeau type; Schwartz distributions; nonlinear theory of generalized functions; differential geometry; partial differential equations; geometry; relativity PDFBibTeX XMLCite \textit{M. Grosser} et al., On the foundations of nonlinear generalized functions. I, II. Providence, RI: American Mathematical Society (AMS) (2001; Zbl 0985.46026) Full Text: DOI arXiv