2001/02/14 by Aline Bonami, Bonami, Aline, Bruno Demange +3 · 5 citations
Engineering · Mathematics · Physics and Astronomy · #32A15 #42B10 #94A12 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Sparse and Compressive Sensing Techniques #math-ph #math.CA #math.MP #msc:32A15 #msc:42B10 #msc:94A12
paper · pdf · doi:10.48550/arxiv.math/0102111
22 pages, submitted
arxiv created 2001/02/14 · openalex publication_date 2001/02/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on \Rd which may be written as P(x)exp (Ax,x), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We also give the best constant in uncertainty principles of Gelf'and Shilov type. 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.