Some integrals for cosine families of bounded linear operators on some non-Archimedean Banach spaces [Articol]

Abstract

In this paper, we define and study the Volkenborn integral and the Shnirelman integral for cosine families of bounded linear operators on some non-Archimedean Banach spaces over Qp and Cp respectively. We give some functional calculus for cosine families of infinitesimal generator A such that A is a nilpotent operator on some non-Archimedean Banach spaces over Cp. Many results are proved and examples are given to support our work.