We develop an elementary theory of Fourier and Laplace transformations for exponentially decreasing hyperfunctions. Since any hyperfunction can be extended to an exponentially decreasing hyperfunction, this provides simple notions of asymptotic Fourier and Laplace transformations for hyperfunctions, improving the existing models. This is used to prove criteria for the uniqueness and solvability of the abstract Cauchy problem in Fréchet spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-4,
author = {Michael Langenbruch},
title = {Asymptotic Fourier and Laplace transformations for hyperfunctions},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {41-69},
zbl = {1225.44001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-4}
}
Michael Langenbruch. Asymptotic Fourier and Laplace transformations for hyperfunctions. Studia Mathematica, Tome 204 (2011) pp. 41-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-4/