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Spectral analysis on upper light cone in $$R^ 3$$ and the Radon transform. (English) Zbl 0684.43005
Let G be the Lorentz group SO(2,1). In the usual notation of the subject [see S. Helgason, Groups and geometric analysis (1984; Zbl 0543.58001)] the author considers the upper hyperboloid $$H=G/K$$ and the upper light cone $$L=G/N$$. The Radon transform on H and the dual Radon transform on L as well as the Fourier transform on H are introduced. The study of spectral analysis in L is pursued and it is found that not only continuous series but also finite dimensional and discrete series representations of G appear. A theorem of Pompeiu type is formulated for L. That is a necessary and sufficient condition for a compactly supported distribution on L to span a dense subset of $${\mathcal E}(L)$$ by translations and linear combinations.
Reviewer: A.Terras

##### MSC:
 43A85 Harmonic analysis on homogeneous spaces 43A80 Analysis on other specific Lie groups 22E43 Structure and representation of the Lorentz group 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
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