International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 5, Pages 52398, 9 p.
doi:10.1155/IJMMS/2006/52398
C0-semigroups of linear operators on some ultrametric Banach spaces
Toka Diagana
Department of Mathematics, Howard University, 2441 6th Street, NW Washington 20059, DC, USA
Abstract
C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.