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

Marat V. Markin

 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

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.