$C_{0}$-Groups and $C$-Groups on Non-Archimedean Quasi-Banach Spaces

Document Type : Research Article

Author

C. High school of Hauman El fetouaki, Had Soualem, Morocco

Abstract

In this paper, we introduce and study  $C_{0}$-groups and $C$-groups of bounded linear operators on non-Archimedean quasi-Banach spaces over $\mathbb{K}.$ In particular,  we show some results related to them. In contrast with the classical framework, the parameter of $C_{0}$-groups and $C$-groups families of bounded linear operators belongs to a open ball $\Omega_{r}$ of a non-Archimedean field $\mathbb{K}.$ As an illustration, we shall discuss the solvability of some homogeneous $p$-adic differential equations for $C_{0}$-groups and $C$-groups. Also, we provide some examples to illustrate our study.

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References

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 1
May 2024
Pages 114-132

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History

  • Receive Date: 02 June 2025
  • Revise Date: 01 July 2025
  • Accept Date: 18 July 2025
  • Publish Date: 07 August 2025

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