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## Tensor valued Colombeau functions on manifolds

### Volume 88 / 2010

Banach Center Publications 88 (2010), 145-152 MSC: Primary 46F30; Secondary 46T30, 53A45 DOI: 10.4064/bc88-0-11

#### Abstract

Extending the construction of the algebra $\hat{\mathcal G}(M)$ 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.

#### Authors

• M. GrosserFaculty of Mathematics
University of Vienna
Nordbergstraße 15
A-1090 Wien, Austria
e-mail

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