7 problems

Let $\alpha(\omega)$ denote the norm of $W(-\nu_{0}+i\omega)$, where $W$ is the operator-valued function defined in the preceding construction. Asymptotic almost periodicity conjec…

Let $f\in B_2\cap C(\mathbb{R},\mathbb{C})$ satisfy the linear independence condition and assume either the condition ensuring continuous sample paths of $\mathcal{M}_f$, or the tw…

Let $u(t,x)$ solve the KdV equation … Assume that the initial data $u(0,x)$ is almost periodic in $x$. Deift's conjecture. The solution $u(t,x)$ is almost periodic in time $t$ and…

Outer-function characterization. The function $h$ above is outer if and only if $F$ has no zeros in the open upper half-plane.

Bounded-constant conjecture. In the estimate above, $C_n$ can be replaced by a bounded sequence.

Strichartz's conjecture. There exists a uniformly almost periodic function $g$ such that

Asymptotic semi-periodicity conjecture. If $f$ is periodic, then for every $t$ the sequence $\eta_n(t)$ is asymptotically semi-periodic. If $f$ is almost periodic, then for every…