Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions

Andreas U. Schmidt

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-34

Abstract:

We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these asymptotic and tempered hyperfunctions to known classes of test functions and distributions, especially the Gel'fand-Shilov spaces. Further it is shown that the asymptotic hyperfunctions, which decay faster than any negative power, are precisely the class that allows asymptotic expansions at infinity. These asymptotic expansions are carried over to the higher-dimensional case by applying the Radon transformation for hyperfunctions.

Date: 2005
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2005/264261.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2005/264261.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:264261

DOI: 10.1155/IJMMS.2005.755

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().