We consider generalizations of the classical Fourier uniqueness theorem. First, we construct a family of uniformly discrete sets $\Lambda \subset \mathbb{R}$, of uniform density one, such that the exponential system $\{e^{2\pi i\lambda x} : \lambda \in \Lambda\}$ is complete in $L^p(S)$ for every $1 \leq p<\infty$ and...
Susanna Bertolini, Enric Florit-Simon, Lukas Liehr et al.· 0 citations
We characterize all lattices $\Lambda \subset \mathbb{R}^2$ of rational density for which the Gabor system generated by the first Hermite function along $\Lambda$ is a frame for $L^2(\mathbb{R})$. We prove that these are precisely the lattices whose density satisfies $D(\Lambda) = \frac{q}{p} $ where $p,q \in \mathbb{N...
Lukas Liehr, Irina Shafkulovska, Mitchell A. Taylor· 1 citation· ⚡1
We establish a sharp version of Grothendieck's theorem for Bessel sequences. Precisely, given a Bessel sequence $\{ x_j \}_{j\in\mathbb{N}}$ with Bessel bound $1$ in a Hilbert space, we show that there exists functions $\{ f_j \}_{j\in\mathbb{N}}$ belonging to the unit ball of $L^\infty([0,1])$ such that for all $j,k \...
Lukas Liehr, Mitchell A. Taylor, Peiyang Yu· 1 citation
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