We study the robustness properties of strong stability of a strongly continuous semigroup on a Hilbert space. We concentrate on a situation where the generator of the unperturbed semigroup has a finite spectral point on the imaginary axis and the resolvent operator is polynomially bounded elsewhere on the imaginary axis. As our main result we present conditions for preservation of the strong stability of the semigroup under bounded perturbations.
CITATION STYLE
Paunonen, L. (2015). On robustness of strongly stable semigroups with spectrum on iℝ. In Springer Proceedings in Mathematics and Statistics (Vol. 113, pp. 105–121). Springer New York LLC. https://doi.org/10.1007/978-3-319-12145-1_7
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