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On the definition of neutrix product of generalized functions on \(C^ \infty\)-manifolds. (English) Zbl 0829.46024

The author considers the space \({\mathcal D}' (M)\) of generalized functions (distributions) on a smooth \(m\)-manifold \(M\), each defined by a collection of “compatible” ordinary distributions given on the charts of some \(C^\infty\) atlas on \(M\). In the present paper an extension of the definition of the neutrix distribution product is given based on van der Corput’s notion of neutrix limits onto the space \({\mathcal D}' (M)\). Two theorems are proven concerning the existence of the neutrix distribution product in \({\mathcal D}' (M)\) using different hypotheses for the neutrix product of the distribution components.
This article is mainly an announcement of results.

MSC:

46F10 Operations with distributions and generalized functions
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