4 problems

Uniform Littlewood conjecture. For any real numbers $xi,zeta$,

Let $\xi$ be a transcendental real number and let $n$ be a positive integer. The uniform exponent of approximation $\widehat{\omega}_n(\xi)$ is the supremum of the real numbers…

Let $\mathcal L\in\operatorname{\mathcal S\mathcal E}$, and let $X$ be a compact set in $\mathbb C$. The spaces $P_{\mathcal L}(X)$ and $C_{\mathcal L}(X)$ denote, respectively, th…

Let $n$ be a positive integer and let $\boldsymbol{\zeta}=(\zeta_1,\ldots,\zeta_n)\in\mathbb{R}^n$ be such that $1,\zeta_1,\ldots,\zeta_n$ are linearly independent over…