Year: 2025
Type: article
Abstract: Metaplectic time-frequency representations are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question of which metaplectic time-frequency representations satisfy an uncertainty principle in the style of Benedicks and Amrein–Berthier. That is, if the metaplectic time-frequency representation is supported on a set of finite measure, must the functions then be zero? While this statement holds for the short-time Fourier transform, it is false for some other natural time-frequency representations. We provide a full characterization of the class of metaplectic time-frequency representations which exhibit an uncertainty principle of this type, both for sesquilinear and quadratic versions.
Source: Journal d Analyse Mathématique
Authors: Karlheinz Gröchenig, Irina Shafkulovska
Institution: University of Vienna
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Austrian Science Fund
OpenAlex ID: W7114773749