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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.

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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References:

[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.
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