Asymptotic Hyperfunctions, Tempered Hyperfunctions, and Asymptotic Expansions

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dc.creatorSchmidt, Andreas U.
dc.date2001-07-07
dc.date2005-05-30
dc.date.accessioned2026-07-07T04:42:31Z
dc.date.available2026-07-07T04:42:31Z
dc.descriptionWe 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 Gelfand-Shilov-Spaces. Further it is shown that the asymptotic hyperfunctions, which decay faster than any negative power, are precisely the class that allow asymptotic expansions at infinity. These asymptotic expansions are carried over to the higher-dimensional case by applying the Radon transformation for hyperfunctions.
dc.description31 pages, 1 figure, typos corrected, references added
dc.identifierhttps://arxiv.org/abs/math/0107058
dc.identifierhttp://arxiv.org/abs/math/0107058
dc.identifierInternational Journal of Mathematics and Mathematical Sciences 2005:5 (2005) 755-788
dc.identifierdoi:10.1155/IJMMS.2005.755
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61818
dc.subjectFunctional Analysis
dc.subjectComplex Variables
dc.subject46F15 (Primary) 46F20, 30E15 (Secondary)
dc.titleAsymptotic Hyperfunctions, Tempered Hyperfunctions, and Asymptotic Expansions
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