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).
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Zwart, H. Growth Estimates for exp(A-1t) on a Hilbert Space. Semigroup Forum 74, 487–494 (2007). https://doi.org/10.1007/s00233-006-0679-1
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DOI: https://doi.org/10.1007/s00233-006-0679-1