- Info
Yury Belov
St. Petersburg State University, Russia
The Newman-Shapiro problem and spectral synthesis in Fock space
In 1966 D. Newman and H. Shapiro posed the following problem.
Let $G$ be a function from Fock space $\mathcal{F}$ and such that
$e^{zw}G\in\mathcal{F}$ for any $w\in\mathbb{C}$. Is it true that
$$Span{FG; FG ∈ F} = Span{e^{wz}G : w ∈ C}?$$
Recently the author (joint with A.Borichev) has constructed a counterexample to this conjecture.
On the other hand, we are able to show that if $G$ satisfies some regularity conditions, then
conjecture holds. These results are clоsеly connected to some
spectral synthesis problems in Fock space.