The abstract Cauchy problem in locally convex spaces

Abstract

We derive sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results of Langenbruch beyond the class of Fréchet spaces.

References in corpus (2)

• On equicontinuity and tightness of bi-continuous semigroups
• Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions