Affiliation:
1. Instituto de Matemáticas Universidad de Talca Talca Chile
Abstract
In this paper, we introduce the notion of a
‐discrete semigroup
generated by a closed linear operator
in a Banach space
. We show that
allows us to write the solution to an abstract discrete difference equation of first order as a discrete variation of parameters formula. Moreover, we study the main properties of
and its relation with the well‐known notion of discrete semigroups. Finally, we characterize uniform exponential stability of a
‐semigroup
in terms of the
‐discrete semigroup
.
Subject
General Engineering,General Mathematics