International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 45, Pages 2401-2422
doi:10.1155/S0161171204311105
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 Marat V. Markin. 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.
Abstract
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.