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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).
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