Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms

@article{Bonami2001HermiteFA,
  title={Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms},
  author={A. Bonami and B. Demange and P. Jaming},
  journal={Revista Matematica Iberoamericana},
  year={2001},
  volume={19},
  pages={23-55}
}
  • A. Bonami, B. Demange, P. Jaming
  • Published 2001
  • Mathematics, Physics
  • Revista Matematica Iberoamericana
  • 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 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… CONTINUE READING
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