10 papers
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…
Counterexamples to Schiffer's Conjecture
Gonzalo Cao-Labora, Jaume de Dios Pont
The Schiffer conjecture states that if a smooth domain admits a Neumann eigenfunction of the Laplacian which is constant at the boundary, then the domain is…
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 with a continuous, integrable totally positive function and lattice parameters $α…
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 does not admit a Fourier frame whenever is an odd integer. In particular, this answers a question of Strichartz on the existe…
Stable Phase Retrieval for Spans of Independent Random Variables
Pedro Abdalla, Jaume de Dios Pont, João P. G. Ramos +1
We prove that, after normalization, stable phase retrieval holds over the -spans of independent real-valued centered random variables if and only if all but possibly one…
Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product
Mufan Li, Jaume de Dios Pont, Mihai Nica +1
We study the squared singular value spectrum of a non-square product of independent real Gaussian matrices, equivalently the feature covariance spectrum of a deep linear neural net…