2001/07/31 by Andreas U. Schmidt
Mathematics · #math.FA #math.CV #msc:46F15 #msc:46F20 #msc:30E15
paper · pdf · doi:10.1155/ijmms.2005.755
published as International Journal of Mathematics and Mathematical Sciences 2005:5 (2005) 755-788 · 31 pages, 1 figure, typos corrected, references added
arxiv created 2005/05/30 · arxiv updated 2009/11/30
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 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.