A uniqueness theorem of Beurling for Fourier transform pairs

@article{Hrmander1991AUT,
  title={A uniqueness theorem of Beurling for Fourier transform pairs},
  author={L. H{\"o}rmander},
  journal={Arkiv f{\"o}r Matematik},
  year={1991},
  volume={29},
  pages={237-240}
}
  • L. Hörmander
  • Published 1991
  • Mathematics
  • Arkiv för Matematik
  • There are many theorems known which state that a function and its Fourier transform cannot simultaneously be very small at infinity, such as various forms of the uncertainty principle and the basic results on quasianalytic functions. One such theorem is stated on page 372 in volume II of the collected works of Arne Beurling [1]. Although it is not in every respect the most precise result of its kind, it has a simplicity and generality which make it very attractive. The editors state that no… CONTINUE READING
    Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
    • 135
    • PDF
    The uncertainty principle: A mathematical survey
    • 621
    • Highly Influenced
    Uncertainty principles on certain Lie groups
    • 85
    Uniqueness properties of solutions to Schrödinger equations
    • 44
    • PDF
    A survey on uncertainty principles related to quadratic forms.
    • 36
    A survey on uncertainty principles related to quadratic forms
    • 34
    • PDF
    The sharp Hardy uncertainty principle for Schrödinger evolutions
    • 43
    • Highly Influenced
    • PDF
    Uncertainty principles like Hardy's theorem on some Lie groups
    • 45
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-3 OF 3 REFERENCES
    The Collected Works of Arne Beurling
    • 159
    • PDF
    Fourier transforms of rapidly increasing functions and questions of uniqueness of the solution of Cauchy's problem, Uspekhi ~Iat
    • 1953
    Generalized functions, 2, Moscow, 1958 (Russian)
    • 1968