3 problems

Let $Q(x)<0$ on some interval $(0,x_0)$. Suppose that $Q(x)$ changes sign one or more times as $x$ increases, eventually decays to zero as $x\rightarrow\infty$, and satisfies…

Characteristic-function rearrangement conjecture. For every measurable $A$ with $|A|<\infty$ and every $W>0$,

Let $T,W>0$. For a function $f\in L^2(\mathbb{R})$ with $\|f\|_2=1$ and $|\operatorname{supp}f|\leq T$, consider its quadratic spectral concentration … Here…