Аннотация:
New spaces of rapidly decreasing infinitely differentiable functions on ${\mathbb R}^n$ will be
defined in the talk. They are introduced with a help of a family of separately radial convex
functions on ${\mathbb R}^n$ satisfying some technical conditions and very similar in
construction to Gelfand–Shilov spaces $S_{\alpha}$. For all of them Paley–Wiener type
theorems are obtained. Using some recent facts of convex analysis it will be shown that the
Gelfand-Shilov space $W_M$ is a particular case of one of these spaces.
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