Abstract
In this work, it is shown that a strongly continuous semigroup generated by a normal operatorN is conjugate to the semigroup generated by the real part ofN, provided zero is not an eigenvalue of the real part ofN. It is also shown that in caseN satisfies a certain sectorial property, the homeomorphism establishing the conjugacy, as well as its inverse, is locally Hölder continuous. Moreover, in caseN satisfies the sectorial property and the real part ofN has a pure point spectrum with an at most countable number of eigenvalues, the homeomorphism and its inverse are Lipschitz continuous.
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Rosa, R. Conjugacy of strongly continuous semigroups generated by normal operators. J Dyn Diff Equat 7, 471–490 (1995). https://doi.org/10.1007/BF02219373
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DOI: https://doi.org/10.1007/BF02219373