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Tensor valued Colombeau functions on manifolds

M. Grosser (2010)

Banach Center Publications

Extending the construction of the algebra ^ ( 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...

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