On systems with regular singularities, and their solutions

In this article two problems are solved.
1. It is shown that there exists an exponential representation for the fundamental matrix of a Pfaffian system on $C^n$ with regular singularities on a reducible algebraic submanifold $L$.
2. Let there be given on an algebraic manifold $X$ a function $f(x)$ of the Nilsson class with branch manifold $L\subset X$. It is shown that in a neighborhood of an ordinary point or of a point of normal intersection of components of $L$ the function $f(x)$ generates a $\mathscr D_X$-module with regular singularities on $L$.
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