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arXiv · 2112.02677

The abstract Cauchy problem in locally convex spaces

Karsten Kruse
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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 Fr\'echet spaces.

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Karsten Kruse. 2021-12-05. The abstract Cauchy problem in locally convex spaces. https://doi.org/10.1007/s13398-022-01295-5

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