Conjugacy of Strongly Continuous Semigroups Generated by Normal Operators
نویسنده
چکیده
In this work, we show that a strongly continuous semigroup generated by a normal operator N is conjugate to the semigroup generated by the real part of N , provided zero is not an eigenvalue of the real part of N . We also show that in case N satisfies a certain sectorial property, the homeomorphism establishing the conjugacy, as well as its inverse, is locally Hölder continuous. Moreover, in case N satisfies the sectorial property and the real part of N 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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