Riemann-Liouville transform and linear differential equations on the Riemann sphere

Abstract

We study the Riemann-Liouville transformation of solutions to linear differential equations on the Riemann sphere. The transformation corresponds to the middle convolution of the equations. Under the transformation, we examine the asymptotic behavior of the solutions at the singular points of the equations. When the singular points are regular, we studied it in \cite{Ow} and solved a connection problem for the general rigid Fuchsian equations. In this paper we mainly study the case when some singular points are irregular.