5 problems

Let $d\geq 1$ and let $f\in L^2(\mathbb{R}^d)$ be nonzero. A sequence of pure translates of $f$ is a sequence of the form $(f(\cdot-\lambda_n))_{n\geq 1}$ for…

Let $\mathcal{G}_N(\phi_i,\Lambda_i)$ be a Gabor system in $L^2(\mathbb{R}^d)$, where the disjoint union $\bigcup_{i=1}^N\Lambda_i$ is formed from the parameter sets…

Let a Daubechies filter have length at least $4$, and let its associated basic wavelet packets be the functions obtained from the corresponding low-pass/high-pass filter pair. For…

Let $X$ be a Banach space with a Schauder basis. An operator $T\in\mathcal{B}(X)$ is called strongly TDZ if there exists a sequence $\{T_n\}_{n=1}^\infty$ in $\mathcal{B}(X)$ such…

Pełczyński's conjecture. If $p\neq 2$, then the characters in $L^p({\bf T}^\infty)$ do not form a Schauder basis under any permutation.