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A Hille-Yosida-Phillips Theorem for Discrete Semigroups on Complete Ultrametric Locally Convex Spaces

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Abstract

Let \(E\) be a complete Hausdorff locally convex space over \(\mathbb{C}_{p},\) let \(A\in\mathcal{L}(E)\) such that \((I-\lambda A)^{-1}\) is analytic on its domain. In this paper, we give a necessary and sufficient condition on the resolvent of \(A\) such that \((A^{n})_{n\in\mathbb{N}}\) is equi-continuous.

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References

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Jawad Ettayb

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  1. Jawad Ettayb
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Correspondence to Jawad Ettayb.

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Ettayb, J. A Hille-Yosida-Phillips Theorem for Discrete Semigroups on Complete Ultrametric Locally Convex Spaces. P-Adic Num Ultrametr Anal Appl 15, 113–118 (2023). https://doi.org/10.1134/S2070046623020048

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  • DOI: https://doi.org/10.1134/S2070046623020048

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