International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 52398, 9 pages
-semigroups of linear operators on some ultrametric Banach spaces
Department of Mathematics, Howard University, 2441 6th Street, NW Washington 20059, DC, USA
Received 20 August 2005; Revised 28 February 2006; Accepted 25 April 2006
Copyright © 2006 Toka Diagana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
-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 -semigroups on (ultrametric) free Banach spaces . In contrast with the classical setting, the parameter of a given -semigroup belongs to a clopen ball of the ground field . As an illustration, we will discuss the solvability of some homogeneous -adic differential equations.