Kruse, KarstenKarstenKruse2022-07-262022-07-262022-07-22Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 116 (4): 155, 1-23 (2022)http://hdl.handle.net/11420/13269We 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.en1579-150520224123Springerhttps://creativecommons.org/licenses/by/4.0/abstract Cauchy problemasymptotic Laplace transformasymptotic resolventhyperfunctionMathematikJournal Article10.15480/882.449910.1007/s13398-022-01295-510.15480/882.44992112.02677Other