- We show that the abscissa of convergence of the Laplace transform of an exponentially bounded function does not exceed its abscissa of boundedness. For C0-semigroups of operators, this result was first proved by L. Weis and V. Wrobel. Our proof for functions follows a method used by J. van Neerven in the semigroup case. P.H. Bloch gave an example of an integrable function for which the result does not hold. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.
- Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
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Convergence of Laplace integrals
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