Abstract
We characterize polynomial growth of a C0-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes C0-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups.
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Eisner, T., Zwart, H. A Note on Polynomially Growing C0-Semigroups. Semigroup Forum 75, 438–445 (2007). https://doi.org/10.1007/s00233-007-0723-9
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DOI: https://doi.org/10.1007/s00233-007-0723-9