Abstract
Our aim is to construct hyperfunctions so that they have as close a relation as possible to ordinary functions. Of the operations of addition, subtraction, multiplication and division, the first two are, of course, possible as linear combinations. There are, however, problems with multiplication and division. It may even seem meaningless to consider products of hyperfunctions in a theory such as the Schwartz distribution theory which is based on linear operations. (Indeed, the author thought so, initially.) One of the reasons for the misunderstanding is perhaps the fact that the square δ(x)- δ(x) of a typical hyperfunction δ(x) cannot be reasonably defined.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Imai, I. (1992). Product of Hyperfunctions. In: Applied Hyperfunction Theory. Mathematics and Its Applications (Japanese Series), vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2548-2_12
Download citation
DOI: https://doi.org/10.1007/978-94-011-2548-2_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5125-5
Online ISBN: 978-94-011-2548-2
eBook Packages: Springer Book Archive