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<p>The definition of the Laplace transform of a bounded Radon measure on an Abelian topological semigroup is due to N. Bourbaki. In this note, we generalise this definition and prove inverse formulas for the Laplace transform of measures on semilattices of open-and-compact sets in both discrete and non-discrete cases. These are partial answers to a question posed by Yu.&#xa0;I.&#xa0;Lyubich.</p>

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On the Laplace transform on semilattices

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • A. R. Mirotin

摘要

The definition of the Laplace transform of a bounded Radon measure on an Abelian topological semigroup is due to N. Bourbaki. In this note, we generalise this definition and prove inverse formulas for the Laplace transform of measures on semilattices of open-and-compact sets in both discrete and non-discrete cases. These are partial answers to a question posed by Yu. I. Lyubich.