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Uncertainty principles like Hardy’s theorem on some Lie groups. (English) Zbl 0930.22009
Harmonic analysis on the Heisenberg nilpotent Lie group is not only concerned with quantum physics but also with information transmission channels [W. Schempp, Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory. Pitman Research Notes in Mathematics Series, Vol. 147 (London 1986; Zbl 0632.43001)]. Based on Hardy’s theorem which specifies the impossibility of simultaneous smallness of a nonzero function and its Fourier transform [G. H. Hardy, J. Lond. Math. Soc. 8, 227-231 (1933; Zbl 0007.30403)], the paper under review extends an uncertainty principle to Heisenberg groups, Euclidean spaces, and the Euclidean motion group of the plane. In addition, the paper deals with an analog of Beurling’s theorem in $$\mathbb{R}^n$$ [L. Hörmander, Ark. Mat. 29, 237-240 (1991; Zbl 0755.42009)].
Reviewer: W.Schempp (Siegen)

##### MSC:
 2.2e+26 Nilpotent and solvable Lie groups 2.2e+31 Analysis on real and complex Lie groups