Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
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) . …