, Volume 74, Issue 3, pp 487-494,
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Growth Estimates for exp(A-1t) on a Hilbert Space

Abstract

Let A be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space H. Since A-1 is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by a constant time log(t).