Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
Year: 2003
Type: article
Abstract: We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on \mathbb{R}^d which may be written as P(x)\exp (-\langle Ax, x\rangle) , with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x) \widehat{f}(y) . We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with a sharp version of Heisenberg's inequality for this transform.
DOI: 10.4171/rmi/337
Authors: Aline Bonami, Bruno Demange, Philippe Jaming
Institution: Université d'Orléans
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: European Commission
OpenAlex ID: W2016570961