The abstract Cauchy problem in locally convex spaces

Karsten Kruse*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Downloads (Pure)


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
Issue number4
Publication statusPublished - Oct 2022
Externally publishedYes


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


Dive into the research topics of 'The abstract Cauchy problem in locally convex spaces'. Together they form a unique fingerprint.

Cite this