Mitchell A. Taylor

collaborators

9 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

Stable Phase Retrieval for Spans of Independent Random Variables

Pedro Abdalla, Jaume de Dios Pont, JoÃ£o P. G. Ramos +1

We prove that, after $L^{2}$ normalization, stable phase retrieval holds over the $L^{2}$ -spans of independent real-valued centered random variables if and only if all but possibly one…

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…