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Question. Does there exist an entire function $h$ satisfying three following assertions: $h$ belongs to the $H^2$ Hardy space in every horizontal upper half-plane; $zh - 1$ belongs to $H^2(\mathbb{C}...

Do you know an unbounded open set $A\subset \mathbb{R}^d$, $d\geq 2$ with the following property: if some integrable function $f$ on $\mathbb{R}^d$ has its Fourier transform vanishing on $A^c$ and all ...