Heisenberg’s uncertainty principle in the sense of Beurling
- Haakan Hedenmalm
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We shed new light on Heisenberg’s uncertainty principle in the sense of Beurling, by offering a fundamentally different proof which allows us to weaken the assumptions rather substantially. The new formulation is pretty much optimal, as can be seen from examples. Our arguments involve Fourier and Mellin transforms. We also introduce a version which applies to two given functions. Finally, we show how our approach applies in the higher dimensional setting.
- M. Benedicks, The support of functions and distributions with a spectral gap, Math. Scand. 55 (1984), 285–309.
- M. Benedicks and H. Hedenmalm, Private communication.
- A. Beurling, The Collected Works of Arne Beurling, Vol. 2, Harmonic Analysis, Birkhäuser Boston, Inc., Boston, MA, 1989.
- A. Bonami, B. Demange, and Ph. Jaming, Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms, Rev. Mat. Iberoamericana 19 (2003), 23–55. CrossRef
- F. Canto-Martín, H. Hedenmalm, and A. Montes-Rodríguez, Perron-Frobenius operators and the Klein-Gordon equation, J. Eur. Math. Soc. (JEMS), to appear.
- L. Carleson, Selected Problems on Exceptional Sets, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967.
- G. H. Hardy, A theorem concerning Fourier transforms, J. London Math. Soc. 8 (1933), 227–231. CrossRef
- V. Havin and B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Springer-Verlag, Berlin, 1994. CrossRef
- H. Hedenmalm and A. Montes-Rodríguez, Heisenberg uniqueness pairs and the Klein-Gordon equation, Ann. of Math. (2) 173 (2011), 1507–1527. CrossRef
- L. Hörmander, A uniqueness theorem of Beurling for Fourier transform pairs, Ark. Mat. 29 (1991), 237–240. CrossRef
- Heisenberg’s uncertainty principle in the sense of Beurling
Journal d'Analyse Mathématique
Volume 118, Issue 2 , pp 691-702
- Cover Date
- Print ISSN
- Online ISSN
- The Hebrew University Magnes Press
- Additional Links
- Haakan Hedenmalm (1)
- Author Affiliations
- 1. Department of Mathematics, KTH Royal Institute of Technology, S-10044, Stockholm, Sweden