Tensor Valued Colombeau Functions on Manifolds
Abstract
Extending the construction of the (intrinsically defined) full algebra of scalar valued Colombeau functions on a smooth manifold M (Grosser et al., Adv. Math. 166 (2002), 179-206) 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.
Cite
@article{arxiv.0812.3275,
title = {Tensor Valued Colombeau Functions on Manifolds},
author = {Michael Grosser},
journal= {arXiv preprint arXiv:0812.3275},
year = {2008}
}
Comments
LaTeX, 10 pages, Contribution presented at the International Conference on Generalized Functions, GF07, September 2007, Bedlewo, Poland, final version; to be published in the conference proceedings, Banach Center Publications