Non abelian ramification (Q1385304)

This paper concerns the holomorphic noncharacteristic Cauchy problem \[ a(x, D)u(x)= v(x);\;D^h_{x_0}u(x)|_{x_0= 0}= u_h(x'),\;0\leq h<m,\;x= (x_0,x')\in \mathbb{C}^{n+ 1}, \] for an operator with characteristics of constant multiplicity and ramified data along hypersurfaces. It gives a unified presentation of several results in this domain. The ramification of the right-hand side is arbitrary. A new simplified proof is given for a general result obtained by E. Leichtnam.