Semigroup Forum

, Volume 74, Issue 3, pp 487–494

Growth Estimates for exp(A-1t) on a Hilbert Space

Open Access

DOI: 10.1007/s00233-006-0679-1

Cite this article as:
Zwart, H. Semigroup Forum (2007) 74: 487. doi:10.1007/s00233-006-0679-1


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).

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© Springer 2007

Authors and Affiliations

  1. 1.Department of Applied Mathematics, University of Twente, P.O. Box 2177500 AE EnschedeThe Netherlands

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