Extending the construction of the algebra of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M, via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension of the classical Lie derivative. Its members are smooth functions depending-via a third slot-on so-called transport operators, in addition to slots one (smooth n-forms on M) and two (points of M) from the scalar case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-11,
author = {M. Grosser},
title = {Tensor valued Colombeau functions on manifolds},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {145-152},
zbl = {1202.46051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-11}
}
M. Grosser. Tensor valued Colombeau functions on manifolds. Banach Center Publications, Tome 89 (2010) pp. 145-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-11/