Characterization of Hyperbolic Semigroups

Abstract

In this article, the Banach space is decomposed into the direct sum of two closed subspaces such that the semigroup becomes forward exponentially stable on one subspace and backward exponentially stable on other subspace. Hyperbolic semigroup is characterized in terms of the spectrum of its cogenerator. Further, we study the rescaled hyperbolic semigroup to analyze its spectrum.