The abstract Cauchy problem in locally convex spaces

Karsten Kruse*

*Corresponding author for this work

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Abstract

We derive necessary and 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.

Original languageEnglish
Article number155
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume116
Issue number4
DOIs
Publication statusPublished - Oct 2022
Externally publishedYes

Keywords

  • Abstract Cauchy problem
  • Asymptotic Laplace transform
  • Asymptotic resolvent
  • Hyperfunction

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