The Cayley transform of the generator of a bounded $C_0$-semigroup

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Gomilko, A. and Zwart, H.J. (2007) The Cayley transform of the generator of a bounded $C_0$-semigroup. Semigroup Forum, 74 (1). pp. 140-148. ISSN 0037-1912

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Abstract:Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the Cayley transform $V=(A+I)(A-I)^{-1}$ is a power-bounded operator, i.e., $\sup_{n\in N}\,\|V^n\|\,<\infty.$
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/63698
Official URL:http://dx.doi.org/10.1007/s00233-006-0648-8
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