Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space


Zwart, H.J. (2007) Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space. Semigroup Forum, 74 (3). pp. 487-494. ISSN 0037-1912

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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 times $\log(t)$.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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