Geodesic
Space-like solutions of Gel'fand-Yaglom type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 1, pp. 25-38

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A study is made of the existence of space-like solutions ofGel'fand-Yaglomtype equations of the most general form. For the case when the matrix $\|c_{\tau\tau'}\|$, determining $L^0$ is either nondegenerate or Hermitian and the mass spectrum of time-like states contains no degenerate branches, i.e., $m_i(s)\equiv m_j(s+n)$ ($i\ne j$, $n=0, 1, 2,\dots$), it is shown that there is always a continuum of “masses” corresponding to space-like solutions. For the case when the mass spectrum of time-like states contains degenerate branches a class of equations is given that does not admit space-like solutions. 
@article{TMF_1970_5_1_a2,
     author = {L. M. Slad},
     title = {Space-like solutions of {Gel'fand-Yaglom} type equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {25--38},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_5_1_a2/}
}
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L. M. Slad. Space-like solutions of Gel'fand-Yaglom type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 1, pp. 25-38. http://geodesic.mathdoc.fr/item/TMF_1970_5_1_a2/