Asymptotic Fourier and Laplace transformations for hyperfunctions

@article{MichaelLangenbruch2011,
abstract = {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.},
author = {Michael Langenbruch},
journal = {Studia Mathematica},
keywords = {asymptotic Fourier transformation; asymptotic Laplace transformation; hyperfunction; abstract Cauchy problem; asymptotic resolvent},
language = {eng},
number = {1},
pages = {41-69},
title = {Asymptotic Fourier and Laplace transformations for hyperfunctions},
url = {http://eudml.org/doc/285845},
volume = {205},
year = {2011},
}

TY - JOUR
AU - Michael Langenbruch
TI - Asymptotic Fourier and Laplace transformations for hyperfunctions
JO - Studia Mathematica
PY - 2011
VL - 205
IS - 1
SP - 41
EP - 69
AB - 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.
LA - eng
KW - asymptotic Fourier transformation; asymptotic Laplace transformation; hyperfunction; abstract Cauchy problem; asymptotic resolvent
UR - http://eudml.org/doc/285845
ER -