The Behaviors of Singular Solutions of Partial Differential Equations in Some Class in the Complex Domain
LetL(z ∂ Z )be a linear partial differential operator with holomorphic coefficients in a neighborhoodUofz= 0 in Cd+1andKbe a nonsingular complex hypersurface. Letu(z) be a solution of the equationL(z ∂ Z )u(z) =0, which has singularities onK.In general there are many singular homogeneous solutions. The purpose of the present paper is to introduce a class of partial differential operators and study of the behaviors of homogeneous solutions ofL(z 3)belonging to this class, by restricting the growth properties of singularities onK.
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