Lukas Liehr

activity

20242026

collaborators

11 papers

math.FA2026

Grothendieck's theorem for Bessel sequences

Lukas Liehr, Mitchell A. Taylor, Peiyang Yu

We establish a sharp version of Grothendieck's theorem for Bessel sequences. Precisely, given a Bessel sequence ${x_{j}}_{j \in N}$ with Bessel bound $1$ in a Hilbert spac…

math.FA2026

Banach lattices and phase retrieval: A case study for the use of AI in mathematics

Jaume de Dios Pont, Lukas Liehr, David Muñoz-Lahoz +2

The ability of large language models to assist professional mathematicians has been progressing rapidly. Earlier this year, a group of researchers in Banach lattice theory and phas…

math.FA2026

Gabor Frames of Totally Positive Functions: A Complete Characterization

Jaume de Dios Pont, Karlheinz Gröchenig, Lukas Liehr +2

We prove that the set of time-frequency shifts ${e^{2 π i β l t} g (t - α k) : k, l \in Z}$ with a continuous, integrable totally positive function $g$ and lattice parameters $α…

math.FA2026

Cantor measures with odd base do not admit Fourier frames

Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor

We prove that the Cantor measure with base $b$ does not admit a Fourier frame whenever $b > 1$ is an odd integer. In particular, this answers a question of Strichartz on the existe…

math.FA2026

On the existence problem of regular Gabor frames

Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor

For every dimension $d > 1$ , we establish explicit criteria on lattices $I^ \subset R^{2 d}$ with density $D (I^) > 1$ such that no function with a continuous Zak transform g…

math.FA2026

Compactly supported Gabor orthonormal bases

Lukas Liehr

We characterize all lattices $I^ \subset R^{2}$ and all compactly supported functions $g \in L^{2} (R)$ for which the Gabor system $\left \{ e^{2Ïi s x} g(x-t) : (t,s)…