On the Cauchy-Kowalewski theorem for general system of differential equations (Q1064456)

In [Bull. Soc. R. Sci. Liège 50, 107-114 (1981; Zbl 0475.35004)] the author has given a necessary and sufficient condition in order that the Cauchy-Kowalewski theorem holds for a Cauchy problem \[ A(\partial_ t,\partial_ x)u(t,x)=f(t,x),\quad \partial^ k_ t u_ j|_{t=0}=\phi_{j,k}(x),\quad k=0,1,...,m_ j-1,\quad j=1,2,...,N \] where A is an \(N\times N\) matrix whose entries are partial differential operators with constant coefficients and \(\{m_ 1,...,m_ N\}\) is a given collection of non-negative integers. In the present paper the same problem is discussed for systems \(A(t,x,y,\partial_ t,\partial_ x,\partial_ y)u=f(t,x,y)\) where A is an \(N\times N\) matrix whose entries are partial differential operators with holomorphic coefficients in a neighbourhood of the origin.