Holomorphic solutions of functional differential systems near singular points

Abstract:

Functional analysis techniques are used to prove a theorem, analogous to the Harris-Sibuya-Weinberg theorem for ordinary differential equations, which yields as corollaries a number of existence theorems for holomorphic solutions of linear functional differential systems of the form ${z^D}y’(z) = A(z)y(z) + B(z)y(\alpha z) + C(z)y’(\alpha z)$ in the neighborhood of the singularity at $z = 0$.