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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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[1] Beurling, A.,The collected works of Arne Beurling, 1–2, Birkhäuser, Boston, 1989. · Zbl 0732.01042
[2] Gel’fand, I. M. andShilov, G. E., Fourier transforms of rapidly increasing functions and questions of uniqueness of the solution of Cauchy’s problem,Uspekhi Mat. Nauk 8: 6 (1953), 3–54.
[3] Gel’fand, I. M. andShilov, G. E.,Generalized functions, 2, Moscow, 1958 (Russian). English translation, Academic Press, 1968.
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