期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 440, 期 1, 页码 183-219出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2016.03.022
关键词
Nonlinear generalized functions; Diffeomorphism invariance; Colombeau algebra; Singular pseudo-Riemannian geometry; Covariant derivative
资金
- Austrian Science Fund (FWF) [P23714, P25064]
- Austrian Science Fund (FWF) [P23714, P26859] Funding Source: Austrian Science Fund (FWF)
- Austrian Science Fund (FWF) [P 23714] Funding Source: researchfish
We present an extension of J.F. Colombeau's theory of nonlinear generalized functions to spaces of generalized sections of vector bundles. Our construction builds on classical functional analytic notions, which is the key to having a canonical geometric embedding of vector bundle valued distributions into spaces of generalized sections. This permits to have tensor products, invariance under diffeomorphisms, covariant derivatives and the sheaf property. While retaining as much compatibility to L. Schwartz' theory of distributions as. possible, our theory provides the basis for a rigorous and general treatment of singular pseudo-Riemannian geometry in the setting of Colombeau nonlinear generalized functions. (C) 2016 Elsevier Inc. All rights reserved.
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