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A space of entire functions of several complex variables rapidly decreasingon ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ ismajorized with a help of a family of weight functions is considered in thepaper. For this space an equivalent description in terms of estimates on allpartial derivatives of functions on ${\mathbb R}^n$ and Paley-Wiener typetheorem are obtained.

On a space of entire functions rapidly decreasing on ${\mathbb R}^n$ and its Fourier transformation