On the fundamental matrix of a Pfaffian system of Fuchsian type

A necessary and sufficient condition is given in order that a completely integrable Pfaffian system with regular singular point, given on a polydisk $D^n$, be of Fuchsian type. It is proved that the system is Fuchsian if and only if the space of solutions is “weakly singular”. In the one-dimensional case, this problem was studied by A. H. M. Levelt (RZhMat., 1963, 12B56). For higher dimensions, a similar attempt was made by R. Gérard (RZhMat., 1970, IA553), but his paper contains an error.
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