Smooth solutions of Volterra equations via semigroups

Abstract

In this paper we introduce a class of left shift semigroups that are differentiable. With help of perturbation theory for differentiable semigroups we show that solutions of an integrodifferential equation can be infinitely differentiable if the convolution kernel is sufficiently smooth and regular.

Keywords

• Smooth
• solutions
• Volterra
• equations
• semigroups