Meromorphic representations of the solutions of the singular Cauchy problem. II (Q910944)

[For part I see the author in ibid. 26, 639-646 (1986; Zbl 0628.35054).] The author studies existence and regularity of solutions of the characteristic Cauchy problem \[ (tD^ 2_ t-D^ 2_ x-cD_ t+t\tilde c(t,x)D_ t+a(t,x)D_ x+b(t,x))u=0,\quad u(0,x)=w(x) \] in a small complex neighborhood in \(C^ 2\) of 0. The a, b, \(\tilde c\) are assumed holomorphic in a neighborhood of \(O\in C^ 2\), but w may have a pole at 0. The solution is obtained in a rather constructive way and it is shown that it extends holomorphically to the universal covering space of \(\omega\) \(\setminus K\) where K is constructed from the characteristic curves of the operator and \(\omega\) is a neighborhood of the origin.