Necessary and sufficient conditions for a scalar-type spectral operator in a Banach space to be a generator of a Carleman ultradifferentiable C 0-semigroup are found. The conditions are formulated exclusively in terms of the spectrum of the operator.
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1215–1233, September, 2008.
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Markin, M.V. On scalar-type spectral operators and Carleman ultradifferentiable C 0-semigroups. Ukr Math J 60, 1418–1436 (2008). https://doi.org/10.1007/s11253-009-0141-0
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DOI: https://doi.org/10.1007/s11253-009-0141-0