A uniqueness theorem of Beurling for Fourier transform pairs. (English) Zbl 0755.42009

The author shares with us the proof of a version of the Heisenberg uncertainty principle that was communicated to him verbally by Arne Beurling in the mid-1960’s.


42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Full Text: DOI


[1] Beurling, A., The collected works of Arne Beurling, 1-2 (1989), Boston: Birkhäuser, Boston · Zbl 0732.01042
[2] Gel’fand, I. M.; Shilov, G. E., Fourier transforms of rapidly increasing functions and questions of uniqueness of the solution of Cauchy’s problem, Uspekhi Mat. Nauk, 8, 6, 3-54 (1953) · Zbl 0052.11605
[3] Gel’fand, I. M. andShilov, G. E.,Generalized functions, 2, Moscow, 1958 (Russian). English translation, Academic Press, 1968.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.