Space-like solutions of Gel'fand-Yaglom type equations

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.