Tensor valued Colombeau functions on manifolds

Volume 88 / 2010

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


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.


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image