On the singularities of the solution to the Cauchy problem with singular data in the complex domain

Abstract

This paper is a subsequent one to the author's [8]. The primary objective here is to study the holomorphy of an integral over a certain relative cycle depending on parameters for applications to the study of the singularities of the solution to the Cauchy problem with singular data. Let a(x, 8) (x=(xo . . . . . x,)ell2 "+1) be a linear differential operator with holomorphic coefficients and the initial plane x0 =0 be non-characteristic. We consider the Cauchy problem near the origin of II; "+~ with singular data: