3 problems

Let $n$ be a positive integer and let $\alpha_1,\ldots,\alpha_{2n}$ be real numbers satisfying … Consider the alternating exponential sum $\sum_{j=1}^{2n}(-1)^j e^{i\alpha_jt}$. Al…

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

Let $Q$ be a $d$-dimensional cube and let $f^*$ denote the monotone rearrangement of $f$ on $[0,1]$. Let $c(d)$ be the constant appearing in the dimension-reduction conjecture for…