期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2020.0640
关键词
nonlinear generalized functions; Colombeau algebra; diffeomorphism invariant
资金
- Austrian Science Fund (FWF) [P26859, P30233]
- STFC grant [ST/R00045X]
In this work, we adopt a new approach to the construction of a global theory of algebras of generalized functions on manifolds based on the concept of smoothing operators. This produces a generalization of previous theories in a form which is suitable for applications to differential geometry. The generalized Lie derivative is introduced and shown to extend the Lie derivative of Schwartz distributions. A new feature of this theory is the ability to define a covariant derivative of generalized scalar fields which extends the covariant derivative of distributions at the level of association. We end by sketching some applications of the theory. This work also lays the foundations for a nonlinear theory of distributional geometry that is developed in a subsequent paper that is based on Colombeau algebras of tensor distributions on manifolds.
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