# 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} }

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

118 Citations

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

- Mathematics, Physics
- 2001

- 135
- PDF

An analogue of Hardy’s theorem for very rapidly decreasing functions on semi-simple Lie groups

- Mathematics
- 1997

- 69
- PDF

The sharp Hardy uncertainty principle for Schrödinger evolutions

- Mathematics
- 2009

- 43
- Highly Influenced
- PDF

#### References

##### Publications referenced by this paper.

SHOWING 1-3 OF 3 REFERENCES

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