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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 45, Pages 2401-2422

On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable C0-semigroups

Department of Partial Differential Equations, Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchekivs'ka Street, Kiev 01601, Ukraine

Received 6 November 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0-semigroup are found, the latter formulated exclusively in terms of the operator's spectrum.