• Explicit Representation of Roots on 𝑝-Adic Solenoids and Non-Uniqueness of Embeddability into Rational One-Parameter Subgroups

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      https://www.ias.ac.in/article/fulltext/pmsc/117/04/0443-0455

    • Keywords

       

      Solenoid; root multiplicity; infinite divisibility; one-parameter subgroup; embedding problem; convolution semigroup; uniqueness of embedding.

    • Abstract

       

      This note generalizes known results concerning the existence of roots and embedding one-parameter subgroups on 𝑝-adic solenoids. An explicit representation of the roots leads to the construction of two distinct rational embedding one-parameter subgroups. The results contribute to enlighten the group structure of solenoids and to point out difficulties arising in the context of the embedding problem in probability theory. As a consequence, the uniqueness of embedding of infinitely divisible probability measures on 𝑝-adic solenoids is solved under a certain natural condition.

    • Author Affiliations

       

      Peter Becker-Kern1

      1. Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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