arXiv subjects
Publications and source records attributed to Susanna Bertolini.
We prove that the short-time Fourier transform with Gaussian window performs $L^2$-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean 4 of an extension of our result to $L^2$-local stable phase retrieval for all Hermite windows and all elements in the finite span of the canonical basis vectors is also presented.
In this article, we study a calibrated version of Reifenberg theorem "with holes". In particular we study sets that are suitably approximable at all points and scales by calibrated planes and show that, without any additional hypotheses on $β$-numbers, this implies measure upper bounds and rectifiability. This article follows the main techniques introduced in a previous article, but it allows for holes in the sets under consideration, and is more self-contained.