On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable -semigroups.
Markin, Marat V. (2004)
International Journal of Mathematics and Mathematical Sciences
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Markin, Marat V. (2004)
International Journal of Mathematics and Mathematical Sciences
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Markin, Marat V. (2004)
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We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions...
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