Publishing house / Banach Center Publications / All volumes

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.