13 problems

Let $u$ solve the Korteweg–de Vries (KdV) equation with almost periodic initial data. Deift conjecture. The corresponding solution should evolve almost periodically in time. This c…

Let $\mu$ be a tempered distribution such that both $\mu$ and its Fourier transform $\widehat\mu$ are pure-point Radon measures of locally finite support; such a distribution is ca…

Conjecture. The conjectured conclusion is not included in the supplied statement span.

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…

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

Perturbed KdV almost-periodicity conjecture. For suitable perturbations of KdV and suitable almost periodic initial data $u_0(x)$, the Cauchy problem has a unique global solution…

Let $K(\gamma)$ be the Cantor-type compact set associated with the parameter $\gamma$, and let $\mu_{K(\gamma)}$ denote its corresponding measure. The recurrence coefficients are t…

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…

Let $u_\parallel$ denote the parallel component of the velocity $u$, determined by an elliptic equation posed along magnetic field lines. Suppose the magnetic field lines are dense…

Let $M$ be a compact Riemannian manifold. For points $x,y\in M$, let $\tilde N_{x,y}(\lambda)$ denote the remainder term in the spectral function considered in the paper, and let…

Vu's conjecture. The condition