Geodesic
Some integrals for groups of bounded linear operators on finite-dimensional non-Archimedean Banach spaces
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2022), pp. 3-14 
J. Ettayb. Some integrals for groups of bounded linear operators on finite-dimensional non-Archimedean Banach spaces. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2022), pp. 3-14. http://geodesic.mathdoc.fr/item/BASM_2022_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we extend the Volkenborn integral and Shnirelman integral for groups of bounded linear operators on finite-dimensional non-Archimedean Banach spaces over $\mathbb{Q}_{p}$ and $\mathbb{C}_{p}$ respectively. When the ground field is a complete non-Archimedean valued field, which is also algebraically closed, we give some functional calculus for groups of infinitesimal generator $A$ such that $A$ is a nilpotent operator on finite-dimensional non-Archimedean Banach spaces.

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