Add to ORKGWe 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
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We show that the abscissa of convergence of the Laplace transform of an exponentially bounded functi...
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We establish a resolvent convergence result for the Laplace operator on certain classes of unbound...
Abstract. In this paper, we show convergence and approximation theorem for C-semigroups. And we stud...
Abstract. In this paper, we establish the conditions that a mild C-existence family yields a solutio...
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