Fourier expansion associated with the Lorentz group in the space of functions with support outisde the light cone

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 $S'(R_4)$.