On the fundamental solutions of linear Fuchsian partial differential equations. (English) Zbl 1085.35004

Saito, Toshiaki

J. Math. Soc. Japan 56, No. 4, 1019-1029 (2004).

This paper expresses the solutions given by T. Mandai [J. Math. Soc. Japan 52, 645–672 (2000; Zbl 0993.35004)], for a homogeneous Fuchsian partial differential equation (PDE) with holomorphic coefficients, in the form of an integral involving a kernel which is holomorphic for \(t\) in the universal covering of a pointed disc.

Reviewer: Satyanad Kichenassamy (Reims)

MSC:

35A08	Fundamental solutions to PDEs
35C15	Integral representations of solutions to PDEs

Keywords:

analytic coefficients; homogeneous Fuchsian PDE

Citations:

Zbl 0993.35004