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On Wiener and Levy Type Theorems for System of Characters of the Ring of \(p\)-Adic Integers

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Abstract

We describe the continuous homomorphisms on subalgebras of absolutely convergent series with respect to the character system of \(p\)-adic integers. Using this characterization we obtain Wiener and Levy type theorems for these subalgebras.

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Acknowledgments

The authors thank the referee for valuable remarks and suggestions.

Funding

The work of the first author was supported by the Program of development of Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies” (project no. 075-02-2023-949).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    S. S. Volosivets & A. N. Mingachev

Authors
  1. S. S. Volosivets
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  2. A. N. Mingachev
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Correspondence to S. S. Volosivets or A. N. Mingachev.

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Volosivets, S.S., Mingachev, A.N. On Wiener and Levy Type Theorems for System of Characters of the Ring of \(p\)-Adic Integers. P-Adic Num Ultrametr Anal Appl 16, 136–142 (2024). https://doi.org/10.1134/S2070046624020043

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  • DOI: https://doi.org/10.1134/S2070046624020043

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