Geodesic
Fourier expansion associated with the Lorentz group in the space of functions with support outisde the light cone
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 3, pp. 303-312

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Harmonic analysis on the Lorentz group is constructed in the function space $S(\overline V)$, where $\overline V=R^4\backslash V_+\cup V_-$ ($V_+$ and $V_-$ are, respectively, the future and past light cones). The space $L(\overline V)$, the Fourier transform of $S(\overline V)$, is described. A topological isomorphism between $L(\overline V)$ and $S(\overline V)$ is proved. The results obtained for the space $S(\overline V)$ together with the corresponding results for the spaces $S(\overline V_+)$ and $S(\overline V_-)$ (see [2]) make it possible to construct expansions with respect to irreducible representations of the Lorentz group for generalized functions in $S'(R_4)$. 
@article{TMF_1978_36_3_a1,
     author = {Yu. G. Shondin},
     title = {Fourier expansion associated with the {Lorentz} group in the space of functions with support outisde the light cone},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {303--312},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_36_3_a1/}
}
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Yu. G. Shondin. Fourier expansion associated with the Lorentz group in the space of functions with support outisde the light cone. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 3, pp. 303-312. http://geodesic.mathdoc.fr/item/TMF_1978_36_3_a1/