The space of Fourier hyperfunctions as an inductive limit of Hilbert spaces

Abstract

We research properties of the space of measurable fun- ctions square integrable with weight exp(2ºjxj), and those of the space of Fourier hyperfunctions. Also we show that the several em- bedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hy- perfunctions onto the space of analytic functions extended to any strip in Cn which are estimated with the aid of a special exponential function exp(¹jxj).