Superdistributions
The standard definition of generalized functions (distributions) is generalized to supermanifolds in the frameworks developed in earlier papers of the authors. Having overcome technical obstructions, the authors get a result well-known and obvious if another definition of supermanifold is used (as of a ringed space): since the superspace of functions on a supermanifold is locally the tensor product of the algebra of functions on the underlying space by a finite-dimensional space (Grassmann algebra) V, its dual is the tensor product of the space of distributions on the underlying space by \(V^*\). (The authors in addition identify V with \(V^*\), uncanonically in general case, with the help of Berezin integral over odd variables.)
scientific article; zbMATH DE number 4064092