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<p>In this article, we introduce a class of Lévy processes on certain totally disconnected groups. These processes are described by their Markov transition functions, as in the classical <i>p</i>-adic theory of the Vladimirov operator, and its corresponding Lévy process. An outstanding application of this work is accomplished on the ring of finite adèles, a locally compact topological ring which supports several Vladimirov-type pseudodifferential operators, corresponding to different Lévy processes on it.</p>

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Lévy processes on certain totally disconnected groups

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Víctor A. Aguilar-Arteaga,
  • Miriam Bocardo-Gaspar,
  • Samuel Estala-Arias

摘要

In this article, we introduce a class of Lévy processes on certain totally disconnected groups. These processes are described by their Markov transition functions, as in the classical p-adic theory of the Vladimirov operator, and its corresponding Lévy process. An outstanding application of this work is accomplished on the ring of finite adèles, a locally compact topological ring which supports several Vladimirov-type pseudodifferential operators, corresponding to different Lévy processes on it.