Tauberian theorems and stability of one-parameter semigroups

Authors:
W. Arendt and C. J. K. Batty

Journal:
Trans. Amer. Math. Soc. **306** (1988), 837-852

MSC:
Primary 47D05; Secondary 34G10

DOI:
https://doi.org/10.1090/S0002-9947-1988-0933321-3

MathSciNet review:
933321

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Abstract | References | Similar Articles | Additional Information

Abstract: The main result is the following stability theorem: Let be a bounded -semigroup on a reflexive space . Denote by the generator of and by the spectrum of . If is countable and no eigenvalue of lies on the imaginary axis, then for all .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1988-0933321-3

Keywords:
Tauberian theorems,
-semigroup,
stability,
power bounded,
Laplace transform,
residual spectrum

Article copyright:
© Copyright 1988
American Mathematical Society