A space of entire functions of several complex variables rapidly decreasing on ${ \mathbb R}^n$ and such that their growth along $i{ \mathbb R}^n$ is majorized with a help of a family of weight functions is considered in the paper. For this space an equivalent description in terms of estimates on all partial derivatives of functions on ${ \mathbb R}^n$ and Paley-Wiener type theorem are obtained.
Categories: math.CV math.FA