4 problems

Let $a,b\in \mathbb{R}$ with $0<a<b$. Let $(n_k)_{k \in \mathbb{N}}$ be a strictly increasing sequence of positive integers such that … A non-trivial signed measure with prescribed…

A sequence of positive integers is called a Müntz–Szász sequence when the reciprocal series of its terms diverges. Replication conjecture. For any sequence which is not a Müntz–Szá…

Reverse Müntz–Szász conjecture. If this system is total in $X_p(0,1)$, then $\Lambda$ and $\Lambda'$ are $[-1,1]$-Müntz–Szász sequences.

Irrational-translation density conjecture. If $\theta_1-\theta_2$ is irrational, then $\mathcal{T}_{\Lambda,T}(\cos 2\pi t)$ is dense in the relevant function space under the same…