Analytic solutions of Volterra equations via semigroups

Abstract

We show that solutions of Volterra integrodifferential equations are analytic provided the leading operator generates an analytic semigroup and the convolution kernel is in a space of analytic functions. Similar results have been obtained via Laplace transform, so far.

We show that it is possible to obtain such results using a semigroup approach.

Keywords

• Analytic
• solutions
• Volterra
• equations
• semigroups