5 problems

Let $F$ be a multivariate distribution admitting a density, with the relevant multivariate iteration map and a suitably reformulated version of Theorem 3. Multivariate extension co…

Consider a family of smooth multivariate probability distributions. Multivariate monotonicity conjecture. It should be possible to formulate reasonable conditions under which there…

Improved multivariate indicator-function bound. The inequality above holds for all $m\geq1$.

Bernstein-Nikolskii limit conjecture. The limit

Let $Q^d$ be the $d$-dimensional cube, and let $f$ be a function on $Q^d$. For an integer $k\geq 2$, write $D_x^k f$ for the Peano $k$-th differential at $x$ and $\partial_x^k f$ f…